algorithm
stringclasses
1 value
edge_list
stringlengths
8
5.95k
node_count
int64
3
36
edge_count
int64
1
630
cycle_check
bool
2 classes
triangle_count
int64
0
7.14k
node_degree_node
int64
0
35
node_degree
int64
0
35
connected_nodes_node
int64
0
35
connected_nodes
stringlengths
0
94
edge_existence_src
int64
0
35
edge_existence_dst
int64
0
35
edge_existence
bool
2 classes
reachability_src
int64
0
35
reachability_dst
int64
0
35
reachability
bool
2 classes
shortest_path_src
int64
0
35
shortest_path_dst
int64
0
35
shortest_path
int64
-1
20
erdos
[(0, 1), (0, 4), (0, 5), (0, 6), (1, 2), (1, 4), (1, 5), (1, 6), (1, 7), (2, 4), (2, 7), (2, 8), (2, 9), (2, 12), (3, 5), (3, 13), (3, 14), (4, 6), (4, 8), (4, 11), (5, 6), (5, 14), (6, 11), (6, 14), (6, 21), (7, 15), (7, 16), (8, 9), (8, 10), (8, 11), (9, 10), (11, 21), (12, 17), (12, 18), (12, 19), (13, 14), (14, 21), (15, 16), (15, 23), (15, 24), (16, 17), (16, 20), (16, 24), (17, 18), (17, 23), (18, 19), (18, 22), (19, 22), (20, 24), (23, 24)]
25
50
true
26
3
3
6
0,1,4,5,11,14,21
18
2
false
18
2
true
18
2
2
erdos
[(0, 1), (0, 3), (0, 4), (0, 6), (0, 7), (0, 8), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (2, 12), (2, 13), (2, 14), (2, 15), (3, 4), (3, 6), (3, 8), (3, 13), (4, 5), (4, 6), (5, 11), (5, 12), (5, 14), (5, 15), (6, 7), (6, 8), (7, 8), (7, 25), (7, 26), (8, 25), (8, 26), (9, 10), (9, 11), (9, 12), (9, 22), (9, 27), (10, 11), (10, 22), (10, 27), (11, 12), (11, 22), (11, 27), (12, 14), (12, 15), (13, 14), (13, 20), (13, 21), (13, 30), (14, 15), (14, 20), (16, 17), (16, 18), (16, 19), (17, 19), (17, 20), (17, 21), (18, 19), (20, 30), (21, 28), (21, 29), (21, 30), (22, 27), (23, 24), (23, 25), (23, 26), (24, 25), (24, 26), (25, 26), (28, 29), (29, 30)]
31
73
true
58
6
5
15
2,5,12,14
24
29
false
24
29
true
24
29
6
erdos
[(0, 1), (0, 2), (0, 3), (0, 6), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (2, 3), (2, 6), (2, 8), (2, 9), (2, 10), (3, 8), (4, 14), (4, 15), (5, 6), (5, 16), (7, 11), (8, 14), (9, 10), (11, 12), (11, 16), (12, 13), (14, 15)]
17
26
true
13
12
2
12
11,13
3
9
false
3
9
true
3
9
2
erdos
[(0, 18), (1, 5), (1, 13), (1, 14), (2, 3), (2, 4), (2, 17), (2, 29), (3, 4), (4, 30), (5, 18), (6, 7), (6, 26), (8, 9), (8, 10), (8, 11), (8, 12), (9, 10), (9, 11), (9, 12), (10, 11), (10, 12), (11, 12), (13, 14), (15, 19), (15, 23), (15, 24), (15, 25), (16, 19), (17, 29), (20, 28), (21, 22), (21, 27), (22, 27), (23, 24), (23, 25), (24, 25), (26, 27), (28, 29)]
31
39
true
18
24
3
9
8,10,11,12
0
5
false
0
5
true
0
5
2
erdos
[(0, 9), (0, 11), (1, 8), (1, 14), (2, 4), (2, 15), (3, 9), (5, 9), (6, 8), (6, 15), (7, 17), (7, 18), (8, 13), (10, 14), (12, 18), (14, 16), (14, 17)]
19
17
false
0
17
2
6
8,15
16
3
false
16
3
false
16
3
-1
erdos
[(0, 4), (0, 5), (0, 31), (1, 2), (1, 6), (1, 7), (1, 26), (2, 7), (2, 26), (3, 12), (3, 29), (4, 31), (5, 17), (5, 31), (6, 26), (7, 14), (7, 26), (8, 12), (8, 15), (8, 21), (8, 24), (9, 19), (9, 32), (10, 16), (10, 20), (10, 28), (11, 23), (11, 32), (12, 13), (12, 15), (12, 21), (12, 24), (13, 15), (14, 30), (15, 21), (15, 24), (16, 20), (16, 23), (16, 28), (17, 33), (18, 27), (18, 33), (20, 28), (22, 29), (25, 27)]
34
45
true
19
22
1
30
14
17
31
false
17
31
true
17
31
2
erdos
[(0, 6), (1, 6), (2, 3), (3, 9), (3, 10), (4, 5), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (4, 12), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (8, 9), (8, 10), (9, 10), (9, 11), (10, 11), (11, 12)]
13
29
true
37
5
7
12
4,5,7,11
2
3
true
2
3
true
2
3
1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (2, 3), (2, 5), (2, 6), (3, 4), (3, 5), (3, 7), (4, 8), (5, 6), (5, 7), (5, 24), (5, 28), (5, 29), (6, 17), (6, 20), (6, 24), (6, 28), (7, 29), (8, 30), (9, 10), (9, 11), (9, 14), (9, 15), (10, 11), (10, 12), (10, 13), (10, 14), (11, 13), (11, 14), (11, 15), (12, 15), (12, 16), (12, 17), (14, 18), (15, 16), (16, 17), (16, 20), (17, 20), (18, 33), (19, 26), (21, 22), (22, 27), (23, 28), (23, 29), (24, 25), (24, 26), (25, 27), (28, 29), (31, 32), (31, 33), (32, 33)]
34
55
true
22
26
2
32
31,33
27
18
false
27
18
true
27
18
8
erdos
[(0, 10), (0, 20), (0, 26), (0, 31), (1, 12), (1, 15), (1, 17), (1, 21), (1, 22), (2, 3), (2, 13), (2, 24), (3, 13), (3, 24), (4, 18), (4, 19), (4, 33), (5, 23), (5, 32), (6, 12), (6, 14), (6, 16), (6, 21), (6, 22), (7, 32), (8, 9), (8, 23), (8, 33), (9, 23), (10, 20), (10, 26), (10, 31), (11, 14), (12, 14), (12, 15), (12, 16), (12, 22), (13, 20), (13, 24), (14, 16), (14, 22), (15, 22), (16, 21), (17, 21), (17, 22), (18, 19), (20, 26), (20, 31), (25, 27), (25, 28), (25, 29), (25, 30), (26, 31), (27, 28), (27, 29), (28, 29), (29, 30)]
34
57
true
35
23
3
11
14
25
20
false
25
20
false
25
20
-1
erdos
[(0, 1), (0, 2), (1, 2), (1, 3), (2, 3), (3, 4)]
5
6
true
2
4
1
4
3
2
4
false
2
4
true
2
4
2
erdos
[(0, 2), (0, 3), (0, 4), (1, 5), (2, 3), (2, 4), (5, 9), (5, 12), (5, 19), (6, 8), (7, 8), (8, 13), (8, 15), (8, 18), (9, 11), (9, 12), (10, 16), (10, 17), (12, 14)]
20
19
true
3
9
3
4
0,2
2
8
false
2
8
false
2
8
-1
erdos
[(0, 7), (0, 9), (1, 3), (1, 4), (1, 5), (2, 3), (2, 6), (3, 4), (3, 8), (4, 8), (5, 7), (6, 9)]
10
12
true
2
1
3
1
3,4,5
6
1
false
6
1
true
6
1
3
erdos
[(0, 4), (0, 7), (0, 11), (1, 7), (1, 13), (2, 4), (2, 9), (3, 7), (3, 13), (3, 14), (5, 11), (5, 12), (6, 11), (6, 15), (7, 13), (7, 14), (8, 9), (9, 11), (9, 13), (10, 12), (14, 15)]
16
21
true
3
6
2
6
11,15
2
3
false
2
3
true
2
3
3
erdos
[(0, 1), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 11), (0, 13), (0, 16), (0, 18), (0, 20), (0, 22), (1, 2), (1, 5), (1, 6), (1, 8), (1, 9), (1, 13), (1, 14), (1, 16), (1, 17), (1, 19), (1, 21), (1, 22), (2, 9), (2, 10), (2, 12), (2, 13), (2, 15), (2, 16), (2, 17), (2, 18), (2, 20), (2, 22), (3, 5), (3, 6), (3, 8), (3, 9), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (4, 5), (4, 6), (4, 8), (4, 9), (4, 14), (4, 15), (4, 16), (4, 18), (4, 19), (4, 20), (4, 21), (4, 22), (5, 7), (5, 10), (5, 11), (5, 12), (5, 14), (5, 15), (5, 16), (5, 17), (5, 18), (5, 19), (5, 20), (5, 21), (5, 22), (6, 7), (6, 8), (6, 9), (6, 10), (6, 12), (6, 13), (6, 16), (6, 18), (6, 20), (7, 10), (7, 11), (7, 15), (7, 18), (7, 19), (7, 21), (8, 9), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (8, 20), (8, 22), (9, 10), (9, 13), (9, 15), (9, 18), (9, 20), (10, 12), (10, 13), (10, 14), (10, 16), (10, 17), (10, 18), (10, 19), (10, 20), (10, 21), (10, 22), (11, 17), (11, 21), (11, 22), (12, 13), (12, 14), (12, 15), (12, 17), (12, 18), (12, 20), (13, 14), (13, 15), (13, 16), (13, 17), (13, 18), (13, 20), (13, 22), (14, 16), (14, 17), (14, 19), (14, 20), (14, 21), (15, 16), (15, 18), (15, 19), (15, 20), (15, 22), (16, 17), (16, 20), (16, 21), (17, 19), (17, 20), (17, 21), (17, 22), (18, 20), (18, 21), (18, 22), (19, 21)]
23
147
true
358
5
17
3
0,5,6,8,9,12,13,14,15,16,17
19
12
false
19
12
true
19
12
2
erdos
[(0, 1), (0, 13), (0, 16), (0, 18), (0, 28), (1, 9), (1, 25), (1, 28), (2, 25), (3, 5), (3, 10), (3, 17), (4, 6), (4, 17), (5, 8), (5, 18), (6, 22), (6, 25), (7, 11), (7, 26), (8, 10), (9, 19), (10, 12), (10, 17), (11, 19), (12, 17), (14, 20), (14, 24), (15, 22), (15, 24), (16, 22), (16, 25), (16, 28), (18, 21), (18, 23), (20, 22), (21, 22), (22, 23), (22, 25), (22, 27), (22, 28), (23, 27)]
29
42
true
8
20
2
1
0,9,25,28
15
27
false
15
27
true
15
27
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 6), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (2, 8), (3, 4), (4, 5), (4, 8), (4, 14), (5, 8), (5, 14), (5, 22), (6, 11), (6, 13), (7, 18), (8, 14), (8, 22), (9, 10), (9, 19), (9, 20), (10, 21), (11, 12), (11, 13), (12, 13), (14, 22), (15, 18), (15, 24), (16, 17), (17, 19), (19, 20), (21, 22), (23, 24)]
25
40
true
25
5
6
11
6,12,13
22
2
false
22
2
true
22
2
2
erdos
[(0, 1), (0, 2), (0, 7), (1, 2), (1, 3), (1, 4), (1, 5), (2, 7), (2, 9), (3, 4), (3, 5), (3, 9), (3, 10), (4, 5), (4, 11), (4, 12), (5, 12), (6, 8), (6, 21), (6, 26), (8, 22), (8, 26), (8, 33), (9, 10), (9, 19), (9, 23), (10, 21), (10, 25), (11, 12), (13, 14), (13, 15), (13, 16), (13, 17), (14, 15), (15, 18), (16, 17), (16, 27), (16, 30), (16, 32), (17, 30), (18, 20), (19, 23), (19, 24), (19, 25), (22, 26), (22, 33), (23, 24), (26, 33), (27, 28), (27, 29), (27, 32), (28, 29), (28, 32), (29, 32), (30, 31), (30, 32), (31, 32)]
34
57
true
26
15
3
13
14,15,16,17
25
19
true
25
19
true
25
19
1
erdos
[(0, 2), (1, 2), (2, 4), (3, 4), (3, 5)]
6
5
false
0
0
1
4
2,3
3
4
true
3
4
true
3
4
1
erdos
[(0, 9), (0, 11), (1, 7), (1, 10), (1, 15), (1, 19), (1, 26), (2, 17), (3, 6), (4, 15), (4, 28), (5, 10), (5, 11), (5, 28), (6, 24), (7, 19), (7, 24), (7, 25), (8, 19), (8, 24), (8, 30), (12, 18), (12, 20), (12, 24), (12, 29), (13, 23), (13, 29), (14, 16), (14, 17), (14, 19), (15, 26), (19, 21), (19, 26), (19, 30), (20, 23), (22, 25), (22, 29), (25, 26), (25, 27), (25, 29)]
31
40
true
5
29
4
7
1,19,24,25
9
7
false
9
7
true
9
7
6
erdos
[(0, 2), (0, 5), (0, 6), (1, 14), (1, 16), (2, 4), (2, 5), (2, 6), (2, 7), (3, 5), (3, 7), (3, 10), (3, 20), (4, 5), (4, 6), (5, 6), (5, 8), (7, 10), (8, 9), (8, 13), (8, 17), (8, 18), (11, 12), (11, 13), (11, 15), (11, 17), (12, 14), (12, 15), (12, 17), (13, 15), (14, 16), (19, 20)]
21
32
true
12
19
1
4
2,5,6
12
14
true
12
14
true
12
14
1
erdos
[(0, 2), (0, 3), (1, 4), (2, 4)]
5
4
false
0
4
2
4
1,2
4
2
true
4
2
true
4
2
1
erdos
[(0, 11), (0, 12), (0, 14), (0, 21), (1, 2), (1, 3), (1, 9), (1, 10), (1, 22), (1, 25), (2, 3), (2, 9), (2, 10), (2, 22), (2, 25), (3, 9), (3, 10), (3, 22), (3, 25), (4, 5), (4, 27), (5, 18), (5, 27), (6, 15), (6, 16), (7, 8), (7, 28), (8, 23), (8, 26), (8, 28), (9, 10), (9, 22), (9, 25), (10, 22), (11, 12), (11, 14), (11, 21), (12, 15), (12, 16), (12, 21), (13, 17), (13, 19), (13, 20), (13, 24), (15, 16), (17, 19), (17, 20), (17, 24), (18, 19), (19, 20), (19, 24), (22, 25), (23, 26), (23, 28)]
29
54
true
48
24
3
5
4,18,27
26
1
false
26
1
false
26
1
-1
erdos
[(0, 1), (0, 2), (1, 2)]
3
3
true
1
0
2
0
1,2
1
0
true
1
0
true
1
0
1
erdos
[(0, 1), (0, 4), (0, 13), (0, 20), (1, 5), (1, 14), (1, 16), (1, 21), (2, 13), (3, 10), (3, 23), (4, 12), (4, 21), (5, 9), (6, 12), (6, 18), (7, 10), (7, 20), (7, 24), (8, 10), (8, 15), (8, 20), (9, 12), (9, 18), (9, 20), (9, 24), (10, 17), (10, 24), (11, 17), (11, 20), (11, 24), (13, 16), (13, 24), (14, 19), (14, 24), (15, 18), (16, 22), (19, 24), (21, 22), (22, 23)]
25
40
true
2
21
3
9
5,12,18,20,24
22
24
false
22
24
true
22
24
3
erdos
[(0, 1), (0, 4), (0, 6), (1, 7), (1, 10), (2, 9), (3, 7), (3, 8), (4, 6), (5, 8), (5, 11), (6, 14), (9, 10), (9, 13), (12, 13), (12, 14)]
15
16
true
1
1
3
7
1,3
11
12
false
11
12
true
11
12
9
erdos
[(0, 1), (0, 2), (0, 3), (0, 5), (0, 6), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (2, 7), (2, 8), (3, 5), (3, 6), (4, 22), (5, 6), (5, 7), (5, 16), (6, 7), (6, 15), (6, 16), (7, 14), (7, 15), (7, 16), (7, 24), (8, 17), (8, 20), (8, 24), (8, 25), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (10, 11), (10, 12), (11, 12), (11, 13), (12, 13), (12, 14), (12, 15), (13, 14), (13, 15), (13, 16), (14, 15), (14, 16), (15, 16), (16, 24), (17, 20), (18, 19), (18, 23), (18, 29), (19, 23), (19, 29), (20, 24), (20, 25), (21, 22), (21, 23), (23, 29), (24, 25), (24, 26), (25, 26), (26, 27), (27, 28), (27, 30), (28, 30)]
31
68
true
52
1
5
30
27,28
16
22
false
16
22
true
16
22
4
erdos
[(0, 5), (0, 6), (0, 7), (0, 13), (0, 14), (0, 15), (1, 5), (1, 6), (1, 15), (2, 8), (2, 9), (2, 12), (3, 8), (3, 10), (3, 12), (4, 11), (5, 6), (5, 7), (5, 11), (5, 13), (5, 14), (5, 15), (6, 7), (6, 11), (6, 13), (6, 14), (6, 15), (7, 13), (7, 14), (9, 12), (10, 12), (13, 14), (14, 15)]
16
33
true
32
15
5
1
5,6,15
1
6
true
1
6
true
1
6
1
erdos
[(0, 1), (0, 4), (2, 3), (2, 4), (2, 8), (2, 9), (2, 11), (3, 14), (5, 13), (6, 10), (6, 12), (7, 13), (8, 14), (9, 11), (9, 14), (12, 13)]
15
16
true
1
12
2
5
13
12
14
false
12
14
false
12
14
-1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 6), (0, 7), (0, 13), (1, 2), (1, 3), (1, 4), (1, 5), (2, 6), (2, 17), (2, 18), (3, 4), (3, 5), (3, 11), (3, 12), (4, 13), (4, 14), (4, 16), (5, 11), (5, 12), (6, 7), (6, 23), (7, 9), (7, 10), (7, 13), (7, 15), (7, 23), (8, 10), (8, 15), (8, 20), (8, 24), (9, 10), (9, 13), (10, 13), (10, 15), (11, 12), (11, 27), (12, 16), (12, 27), (12, 29), (12, 30), (13, 14), (13, 15), (14, 15), (14, 16), (15, 19), (16, 29), (17, 18), (17, 28), (19, 20), (21, 22), (23, 24), (25, 26), (26, 28), (29, 30)]
31
58
true
30
3
6
20
8,19
26
29
false
26
29
true
26
29
7
erdos
[(0, 1), (0, 3), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 13), (0, 14), (0, 15), (0, 17), (0, 18), (0, 20), (0, 21), (0, 22), (0, 24), (0, 25), (0, 26), (0, 27), (0, 29), (0, 30), (0, 32), (0, 33), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 12), (1, 13), (1, 15), (1, 17), (1, 18), (1, 20), (1, 21), (1, 22), (1, 23), (1, 25), (1, 27), (1, 28), (1, 30), (1, 31), (1, 32), (2, 3), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 15), (2, 17), (2, 18), (2, 19), (2, 20), (2, 21), (2, 22), (2, 23), (2, 24), (2, 25), (2, 26), (2, 27), (2, 30), (2, 31), (2, 32), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 11), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 18), (3, 20), (3, 22), (3, 23), (3, 24), (3, 25), (3, 26), (3, 27), (3, 28), (3, 29), (3, 30), (3, 31), (3, 32), (3, 33), (4, 5), (4, 7), (4, 9), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (4, 16), (4, 18), (4, 19), (4, 21), (4, 23), (4, 24), (4, 25), (4, 27), (4, 29), (4, 30), (4, 31), (4, 32), (4, 33), (5, 6), (5, 7), (5, 8), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (5, 18), (5, 19), (5, 20), (5, 21), (5, 23), (5, 24), (5, 25), (5, 26), (5, 27), (5, 28), (5, 29), (5, 30), (5, 32), (5, 33), (6, 7), (6, 8), (6, 9), (6, 13), (6, 14), (6, 15), (6, 18), (6, 19), (6, 21), (6, 22), (6, 23), (6, 24), (6, 25), (6, 26), (6, 27), (6, 29), (6, 30), (6, 31), (6, 32), (7, 8), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (7, 18), (7, 19), (7, 20), (7, 22), (7, 23), (7, 25), (7, 26), (7, 27), (7, 28), (7, 29), (7, 30), (7, 31), (7, 32), (8, 9), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (8, 18), (8, 19), (8, 20), (8, 21), (8, 22), (8, 23), (8, 24), (8, 25), (8, 26), (8, 27), (8, 28), (8, 29), (8, 30), (8, 31), (8, 32), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (9, 16), (9, 17), (9, 18), (9, 19), (9, 23), (9, 24), (9, 25), (9, 26), (9, 27), (9, 28), (9, 29), (9, 30), (9, 31), (9, 32), (9, 33), (10, 14), (10, 15), (10, 16), (10, 17), (10, 19), (10, 20), (10, 21), (10, 22), (10, 23), (10, 24), (10, 25), (10, 26), (10, 27), (10, 30), (10, 31), (10, 32), (11, 12), (11, 13), (11, 14), (11, 15), (11, 17), (11, 18), (11, 19), (11, 20), (11, 22), (11, 23), (11, 25), (11, 26), (11, 27), (11, 28), (11, 29), (11, 30), (11, 31), (12, 13), (12, 15), (12, 16), (12, 17), (12, 18), (12, 20), (12, 21), (12, 23), (12, 24), (12, 25), (12, 26), (12, 27), (12, 28), (12, 30), (12, 31), (12, 32), (12, 33), (13, 14), (13, 15), (13, 16), (13, 17), (13, 18), (13, 19), (13, 20), (13, 21), (13, 22), (13, 23), (13, 24), (13, 26), (13, 27), (13, 28), (13, 29), (13, 30), (13, 31), (13, 32), (14, 15), (14, 16), (14, 17), (14, 18), (14, 20), (14, 21), (14, 22), (14, 23), (14, 24), (14, 25), (14, 26), (14, 28), (14, 29), (14, 30), (14, 31), (14, 32), (14, 33), (15, 16), (15, 17), (15, 18), (15, 19), (15, 20), (15, 21), (15, 24), (15, 25), (15, 26), (15, 27), (15, 28), (15, 29), (15, 30), (15, 31), (15, 32), (15, 33), (16, 18), (16, 20), (16, 21), (16, 22), (16, 23), (16, 25), (16, 27), (16, 28), (16, 29), (16, 31), (16, 32), (17, 18), (17, 19), (17, 20), (17, 21), (17, 22), (17, 23), (17, 24), (17, 25), (17, 27), (17, 28), (17, 29), (17, 31), (17, 32), (17, 33), (18, 19), (18, 20), (18, 22), (18, 23), (18, 24), (18, 25), (18, 28), (18, 29), (18, 30), (18, 31), (18, 32), (18, 33), (19, 20), (19, 22), (19, 23), (19, 24), (19, 25), (19, 26), (19, 27), (19, 29), (19, 30), (19, 31), (19, 32), (19, 33), (20, 21), (20, 22), (20, 23), (20, 24), (20, 25), (20, 26), (20, 27), (20, 28), (20, 29), (20, 30), (20, 31), (20, 33), (21, 23), (21, 24), (21, 25), (21, 26), (21, 27), (21, 28), (21, 29), (21, 30), (21, 31), (21, 33), (22, 23), (22, 24), (22, 25), (22, 26), (22, 29), (22, 31), (22, 32), (22, 33), (23, 25), (23, 26), (23, 27), (23, 28), (23, 30), (23, 31), (23, 32), (23, 33), (24, 26), (24, 27), (24, 28), (24, 31), (24, 32), (24, 33), (25, 26), (25, 27), (25, 29), (25, 30), (25, 31), (25, 32), (25, 33), (26, 29), (26, 30), (26, 32), (26, 33), (27, 29), (27, 31), (27, 32), (27, 33), (28, 30), (28, 31), (29, 30), (29, 31), (29, 32), (30, 31), (30, 32), (30, 33), (31, 33), (32, 33)]
34
449
true
3,083
19
25
26
0,2,3,5,6,7,8,9,10,11,12,13,14,15,19,20,21,22,23,24,25,29,30,32,33
26
6
true
26
6
true
26
6
1
erdos
[(0, 1), (0, 3), (1, 5), (1, 13), (1, 15), (2, 5), (2, 6), (3, 14), (4, 6), (4, 10), (4, 12), (7, 11), (7, 15), (8, 17), (9, 10), (9, 18), (11, 14), (11, 16), (12, 13), (12, 16), (13, 16), (15, 16), (17, 18)]
19
23
true
1
3
2
11
7,14,16
7
2
false
7
2
true
7
2
4
erdos
[(0, 1), (0, 2), (1, 2), (1, 6), (1, 11), (1, 13), (1, 15), (1, 16), (2, 15), (3, 10), (3, 15), (4, 5), (4, 8), (4, 15), (4, 16), (4, 21), (4, 22), (5, 7), (5, 12), (5, 21), (6, 16), (6, 20), (7, 8), (7, 10), (7, 13), (8, 13), (8, 16), (8, 17), (8, 18), (9, 13), (9, 19), (10, 13), (11, 15), (14, 15), (14, 16), (16, 18), (16, 20), (21, 22)]
23
38
true
11
1
7
3
10,15
21
3
false
21
3
true
21
3
3
erdos
[(0, 3), (0, 6), (0, 11), (1, 8), (2, 5), (2, 7), (2, 11), (4, 10), (4, 13), (5, 9), (6, 9), (6, 11), (7, 8), (9, 11), (10, 13), (12, 13), (12, 14)]
15
17
true
3
5
2
2
5,7,11
11
8
false
11
8
true
11
8
3
erdos
[(0, 4), (0, 7), (1, 8), (1, 9), (2, 8), (2, 9), (3, 4), (3, 6), (5, 7), (5, 10), (5, 11), (6, 8), (7, 10), (9, 12)]
13
14
true
1
3
2
5
7,10,11
3
11
false
3
11
true
3
11
5
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (3, 6), (3, 7), (4, 5), (4, 6), (5, 6), (5, 8), (6, 8)]
9
18
true
12
6
5
7
2,3
4
2
true
4
2
true
4
2
1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 6), (1, 7), (3, 5), (4, 21), (5, 7), (5, 9), (5, 12), (5, 13), (5, 14), (6, 7), (6, 8), (6, 9), (6, 15), (7, 8), (7, 9), (7, 15), (8, 15), (8, 24), (9, 12), (9, 14), (10, 11), (10, 14), (11, 14), (12, 13), (12, 14), (13, 14), (15, 24), (16, 18), (16, 19), (16, 20), (17, 19), (17, 22), (17, 23), (18, 20), (18, 21), (20, 21), (22, 23)]
25
43
true
21
7
6
16
18,19,20
3
22
false
3
22
true
3
22
8
erdos
[(0, 1), (0, 3), (0, 4), (0, 5), (0, 6), (0, 8), (0, 9), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 3), (2, 4), (2, 5), (2, 6), (2, 8), (2, 9), (3, 4), (3, 7), (3, 8), (3, 9), (4, 6), (4, 7), (4, 8), (4, 9), (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (7, 8), (7, 9), (8, 9)]
10
37
true
64
0
7
4
0,1,2,3,6,7,8,9
6
7
true
6
7
true
6
7
1
erdos
[(0, 3), (0, 7), (0, 13), (0, 14), (0, 17), (0, 18), (0, 23), (0, 25), (0, 29), (1, 7), (1, 13), (1, 16), (1, 23), (1, 25), (1, 28), (2, 17), (2, 29), (3, 5), (3, 6), (3, 7), (3, 8), (3, 13), (3, 15), (3, 23), (3, 25), (3, 27), (3, 29), (4, 6), (4, 7), (4, 8), (4, 11), (4, 13), (4, 14), (4, 15), (4, 16), (4, 20), (4, 21), (4, 23), (4, 25), (4, 26), (4, 27), (4, 29), (5, 9), (5, 19), (6, 21), (6, 24), (6, 28), (7, 10), (7, 14), (7, 21), (7, 28), (8, 9), (8, 21), (9, 15), (9, 29), (10, 14), (10, 15), (10, 18), (10, 23), (10, 26), (11, 21), (12, 14), (12, 15), (13, 14), (13, 15), (13, 21), (13, 28), (14, 15), (14, 20), (14, 22), (14, 23), (14, 25), (15, 21), (15, 28), (15, 29), (18, 21), (18, 22), (19, 29), (20, 24), (21, 23), (21, 25), (21, 29), (23, 28), (24, 27), (25, 28), (28, 29)]
30
86
true
42
0
9
6
3,4,21,24,28
17
16
false
17
16
true
17
16
4
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (3, 4), (3, 5), (3, 6), (3, 7), (4, 5), (4, 6), (4, 7), (5, 6), (5, 7), (6, 7)]
8
28
true
56
2
7
5
0,1,2,3,4,6,7
6
7
true
6
7
true
6
7
1
erdos
[(0, 4), (0, 6), (0, 9), (1, 5), (1, 6), (1, 16), (2, 12), (2, 15), (3, 6), (3, 8), (3, 13), (3, 16), (4, 6), (4, 9), (5, 6), (5, 16), (6, 8), (6, 9), (6, 13), (6, 16), (7, 10), (7, 11), (7, 14), (7, 15), (8, 13), (8, 16), (10, 11), (14, 15)]
17
28
true
17
15
3
15
2,7,14
0
6
true
0
6
true
0
6
1
erdos
[(0, 2), (0, 3), (0, 7), (0, 8), (1, 4), (1, 12), (1, 15), (2, 3), (2, 5), (2, 6), (3, 6), (3, 7), (3, 8), (3, 9), (4, 12), (5, 6), (5, 9), (6, 8), (6, 9), (6, 10), (7, 8), (7, 11), (7, 15), (8, 9), (8, 15), (9, 10), (10, 16), (11, 15), (13, 14), (14, 16)]
17
30
true
16
1
3
8
0,3,6,7,9,15
4
10
false
4
10
true
4
10
5
erdos
[(0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (4, 20), (5, 8), (5, 9), (5, 11), (6, 22), (6, 23), (7, 18), (8, 9), (9, 11), (10, 15), (12, 17), (12, 18), (13, 14), (13, 25), (14, 25), (14, 26), (15, 16), (16, 18), (16, 19), (21, 25), (22, 23), (22, 24), (23, 24), (26, 31), (27, 28), (28, 29), (28, 30), (29, 30), (30, 31)]
32
35
true
7
25
3
9
5,8,11
14
30
false
14
30
true
14
30
3
erdos
[(0, 4), (0, 9), (0, 12), (0, 13), (1, 15), (2, 10), (2, 11), (2, 13), (3, 5), (3, 6), (3, 7), (3, 14), (3, 16), (4, 9), (4, 12), (4, 13), (5, 6), (5, 7), (5, 16), (6, 7), (6, 16), (7, 14), (7, 16), (8, 15), (9, 11), (9, 12), (9, 13), (10, 11), (10, 12), (11, 12), (11, 13), (12, 13), (14, 16)]
17
33
true
29
12
6
1
15
0
11
false
0
11
true
0
11
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (2, 3)]
5
7
true
4
0
4
3
0,1,2
3
4
false
3
4
true
3
4
2
erdos
[(0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (0, 21), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18), (1, 19), (1, 20), (1, 21), (2, 14), (2, 15), (2, 17), (2, 19), (2, 20), (2, 21), (3, 14), (3, 16), (3, 17), (3, 18), (3, 19), (3, 20), (3, 21), (4, 14), (4, 15), (4, 16), (4, 17), (4, 18), (4, 19), (4, 20), (5, 14), (5, 15), (5, 16), (5, 17), (5, 18), (5, 19), (5, 20), (5, 21), (6, 14), (6, 15), (6, 17), (6, 18), (6, 19), (7, 14), (7, 16), (7, 17), (7, 18), (7, 19), (7, 20), (7, 21), (8, 14), (8, 15), (8, 17), (8, 18), (8, 19), (8, 21), (9, 14), (9, 15), (9, 16), (9, 17), (9, 18), (9, 19), (9, 20), (10, 14), (10, 15), (10, 16), (10, 17), (10, 18), (10, 19), (10, 20), (10, 21), (11, 14), (11, 15), (11, 18), (11, 19), (11, 20), (11, 21), (12, 14), (12, 15), (12, 17), (12, 18), (12, 20), (12, 21), (13, 14), (13, 15), (13, 16), (13, 17), (13, 19), (13, 21)]
22
94
true
0
19
13
9
14,15,16,17,18,19,20
12
17
true
12
17
true
12
17
1
erdos
[(0, 1), (0, 2), (0, 4), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 13), (0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (0, 20), (0, 21), (0, 22), (0, 24), (0, 25), (0, 27), (0, 28), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 9), (1, 10), (1, 11), (1, 12), (1, 14), (1, 15), (1, 17), (1, 19), (1, 20), (1, 21), (1, 22), (1, 23), (1, 25), (1, 26), (1, 28), (2, 3), (2, 4), (2, 5), (2, 6), (2, 8), (2, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 14), (2, 15), (2, 17), (2, 18), (2, 19), (2, 20), (2, 22), (2, 23), (2, 24), (2, 27), (2, 28), (3, 5), (3, 6), (3, 8), (3, 9), (3, 10), (3, 11), (3, 13), (3, 15), (3, 16), (3, 17), (3, 18), (3, 19), (3, 20), (3, 21), (3, 23), (3, 26), (3, 28), (4, 5), (4, 6), (4, 7), (4, 9), (4, 10), (4, 11), (4, 14), (4, 18), (4, 19), (4, 20), (4, 21), (4, 23), (4, 24), (4, 25), (4, 27), (4, 28), (5, 11), (5, 12), (5, 14), (5, 15), (5, 16), (5, 17), (5, 18), (5, 20), (5, 21), (5, 22), (5, 25), (5, 26), (5, 27), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (6, 19), (6, 20), (6, 21), (6, 22), (6, 23), (6, 26), (6, 27), (6, 28), (7, 8), (7, 10), (7, 12), (7, 13), (7, 14), (7, 16), (7, 17), (7, 18), (7, 19), (7, 20), (7, 21), (7, 22), (7, 23), (7, 26), (7, 27), (8, 9), (8, 11), (8, 14), (8, 16), (8, 18), (8, 20), (8, 23), (8, 24), (8, 25), (8, 26), (8, 27), (8, 28), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (9, 16), (9, 17), (9, 18), (9, 21), (9, 23), (9, 24), (9, 26), (9, 27), (9, 28), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (10, 19), (10, 23), (10, 24), (10, 27), (10, 28), (11, 14), (11, 15), (11, 17), (11, 19), (11, 21), (11, 22), (11, 24), (11, 27), (12, 14), (12, 15), (12, 16), (12, 17), (12, 18), (12, 19), (12, 21), (12, 22), (12, 23), (12, 24), (12, 25), (12, 26), (12, 27), (12, 28), (13, 14), (13, 16), (13, 17), (13, 18), (13, 19), (13, 20), (13, 23), (13, 24), (13, 25), (13, 28), (14, 15), (14, 16), (14, 17), (14, 18), (14, 19), (14, 20), (14, 21), (14, 22), (14, 23), (14, 24), (14, 25), (14, 26), (14, 28), (15, 17), (15, 18), (15, 19), (15, 20), (15, 21), (15, 22), (15, 23), (15, 24), (15, 25), (15, 26), (15, 28), (16, 17), (16, 20), (16, 24), (16, 25), (17, 19), (17, 20), (17, 21), (17, 22), (17, 23), (17, 24), (17, 26), (17, 27), (17, 28), (18, 19), (18, 21), (18, 22), (18, 23), (18, 24), (18, 26), (18, 28), (19, 20), (19, 21), (19, 22), (19, 23), (19, 24), (19, 25), (19, 26), (19, 28), (20, 21), (20, 22), (20, 25), (20, 26), (20, 27), (20, 28), (21, 22), (21, 23), (21, 25), (21, 27), (21, 28), (22, 25), (22, 27), (23, 24), (23, 26), (23, 27), (23, 28), (24, 25), (24, 26), (25, 26), (25, 27), (26, 27), (26, 28), (27, 28)]
29
290
true
1,347
14
26
6
1,2,3,4,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,26,27,28
1
25
true
1
25
true
1
25
1
erdos
[(0, 3), (0, 4), (0, 6), (0, 7), (1, 2), (1, 29), (2, 23), (3, 4), (3, 5), (3, 7), (4, 5), (4, 17), (6, 7), (6, 27), (6, 28), (7, 26), (7, 27), (7, 28), (8, 9), (8, 10), (8, 11), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (10, 11), (10, 13), (11, 12), (11, 13), (11, 15), (12, 15), (14, 15), (16, 17), (16, 18), (16, 23), (17, 18), (17, 23), (18, 23), (19, 20), (20, 21), (21, 22), (22, 29), (24, 25), (24, 26), (24, 27), (25, 26), (25, 27), (25, 28), (26, 27), (26, 28), (27, 28)]
30
52
true
30
25
4
29
1,22
11
21
false
11
21
false
11
21
-1
erdos
[(0, 1), (0, 2), (0, 3), (0, 6), (0, 7), (0, 8), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (2, 6), (3, 5), (3, 6), (3, 7), (4, 5), (4, 16), (5, 16), (6, 7), (6, 8), (6, 9), (6, 10), (7, 8), (7, 9), (7, 10), (8, 9), (8, 10), (8, 11), (9, 10), (9, 21), (10, 11), (11, 21), (12, 13), (12, 14), (12, 15), (12, 17), (14, 15), (14, 17), (14, 23), (15, 17), (15, 23), (15, 24), (16, 22), (17, 23), (17, 24), (17, 25), (18, 19), (18, 21), (20, 21), (23, 24), (23, 25), (24, 25)]
26
54
true
43
21
4
20
21
11
18
false
11
18
true
11
18
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 13), (0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (0, 20), (0, 21), (0, 22), (0, 23), (0, 24), (0, 25), (0, 26), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (1, 12), (1, 13), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18), (1, 19), (1, 20), (1, 21), (1, 22), (1, 23), (1, 24), (1, 25), (1, 26), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 14), (2, 15), (2, 16), (2, 17), (2, 18), (2, 19), (2, 20), (2, 21), (2, 22), (2, 23), (2, 24), (2, 25), (2, 26), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (3, 18), (3, 19), (3, 20), (3, 21), (3, 22), (3, 23), (3, 24), (3, 25), (3, 26), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (4, 16), (4, 17), (4, 18), (4, 19), (4, 20), (4, 21), (4, 22), (4, 23), (4, 24), (4, 25), (4, 26), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (5, 17), (5, 18), (5, 19), (5, 20), (5, 21), (5, 22), (5, 23), (5, 24), (5, 25), (5, 26), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (6, 19), (6, 20), (6, 21), (6, 22), (6, 23), (6, 24), (6, 25), (6, 26), (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (7, 17), (7, 18), (7, 19), (7, 20), (7, 21), (7, 22), (7, 23), (7, 24), (7, 25), (7, 26), (8, 9), (8, 10), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (8, 19), (8, 20), (8, 21), (8, 22), (8, 23), (8, 24), (8, 25), (8, 26), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (9, 16), (9, 17), (9, 18), (9, 19), (9, 20), (9, 21), (9, 22), (9, 23), (9, 24), (9, 25), (9, 26), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (10, 16), (10, 17), (10, 18), (10, 19), (10, 20), (10, 21), (10, 22), (10, 23), (10, 24), (10, 25), (10, 26), (11, 12), (11, 13), (11, 14), (11, 15), (11, 16), (11, 17), (11, 18), (11, 19), (11, 20), (11, 21), (11, 22), (11, 23), (11, 24), (11, 25), (11, 26), (12, 13), (12, 14), (12, 15), (12, 16), (12, 17), (12, 18), (12, 19), (12, 20), (12, 21), (12, 22), (12, 23), (12, 24), (12, 25), (12, 26), (13, 14), (13, 15), (13, 16), (13, 17), (13, 18), (13, 19), (13, 20), (13, 21), (13, 22), (13, 23), (13, 24), (13, 25), (13, 26), (14, 15), (14, 16), (14, 17), (14, 18), (14, 19), (14, 20), (14, 21), (14, 22), (14, 23), (14, 24), (14, 25), (14, 26), (15, 16), (15, 17), (15, 18), (15, 19), (15, 20), (15, 21), (15, 22), (15, 23), (15, 24), (15, 25), (15, 26), (16, 17), (16, 18), (16, 19), (16, 20), (16, 21), (16, 22), (16, 23), (16, 24), (16, 25), (16, 26), (17, 18), (17, 19), (17, 20), (17, 21), (17, 22), (17, 23), (17, 24), (17, 25), (17, 26), (18, 19), (18, 20), (18, 21), (18, 22), (18, 23), (18, 24), (18, 25), (18, 26), (19, 20), (19, 21), (19, 22), (19, 23), (19, 24), (19, 25), (19, 26), (20, 21), (20, 22), (20, 23), (20, 24), (20, 25), (20, 26), (21, 22), (21, 23), (21, 24), (21, 25), (21, 26), (22, 23), (22, 24), (22, 25), (22, 26), (23, 24), (23, 25), (23, 26), (24, 25), (24, 26), (25, 26)]
27
351
true
2,925
18
26
18
0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26
2
16
true
2
16
true
2
16
1
erdos
[(0, 1), (0, 8), (0, 11), (0, 26), (0, 31), (1, 30), (2, 15), (3, 24), (4, 14), (5, 15), (5, 16), (5, 17), (6, 9), (6, 19), (6, 25), (7, 22), (7, 28), (10, 18), (10, 25), (12, 24), (12, 27), (13, 18), (14, 21), (17, 28), (19, 20), (21, 27), (21, 29), (22, 23)]
32
28
false
0
31
1
10
18,25
15
9
false
15
9
false
15
9
-1
erdos
[(0, 1), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4)]
5
6
true
2
4
2
3
2,4
3
4
true
3
4
true
3
4
1
erdos
[(0, 1), (0, 2), (1, 2), (1, 3), (1, 4), (2, 4), (4, 5)]
6
7
true
2
2
3
2
0,1,4
1
0
true
1
0
true
1
0
1
erdos
[(0, 5), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 14), (0, 15), (1, 2), (1, 3), (1, 4), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (1, 13), (1, 14), (1, 15), (1, 17), (2, 6), (2, 8), (2, 9), (2, 11), (2, 14), (2, 15), (2, 18), (3, 4), (3, 5), (3, 6), (3, 9), (3, 10), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (3, 18), (4, 5), (4, 7), (4, 9), (4, 11), (4, 12), (4, 14), (4, 15), (4, 18), (5, 6), (5, 7), (5, 8), (5, 9), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (5, 17), (5, 18), (6, 7), (6, 10), (6, 12), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (7, 8), (7, 9), (7, 11), (7, 12), (7, 13), (7, 14), (7, 16), (7, 18), (8, 9), (8, 10), (8, 11), (8, 15), (8, 16), (8, 17), (9, 10), (9, 12), (9, 13), (9, 14), (9, 15), (9, 17), (9, 18), (10, 11), (10, 12), (11, 12), (11, 14), (11, 15), (11, 16), (11, 17), (12, 13), (12, 14), (12, 15), (12, 16), (12, 18), (13, 16), (13, 17), (13, 18), (14, 16), (14, 18), (15, 16), (15, 17), (16, 17), (16, 18), (17, 18)]
19
111
true
266
7
12
7
1,4,5,6,8,9,11,12,13,14,16,18
11
6
false
11
6
true
11
6
2
erdos
[(0, 1), (0, 2), (0, 4), (0, 5), (0, 6), (1, 2), (1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 9), (2, 10), (3, 4), (3, 5), (4, 5), (6, 8), (6, 10), (6, 17), (6, 18), (7, 8), (7, 9), (7, 10), (7, 19), (7, 20), (8, 10), (8, 17), (8, 18), (9, 10), (10, 17), (10, 18), (11, 12), (11, 13), (11, 14), (11, 15), (12, 13), (12, 14), (12, 15), (13, 14), (13, 16), (14, 16), (17, 18), (19, 20)]
21
45
true
35
11
4
10
2,6,7,8,9,17,18
0
4
true
0
4
true
0
4
1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (2, 5), (3, 4), (3, 6), (4, 6)]
7
11
true
5
0
5
2
0,1,5
5
2
true
5
2
true
5
2
1
erdos
[(0, 7), (0, 14), (1, 4), (1, 9), (1, 14), (1, 24), (2, 14), (3, 14), (3, 15), (4, 5), (4, 10), (4, 14), (4, 27), (5, 14), (6, 14), (7, 8), (7, 14), (7, 23), (8, 14), (9, 14), (10, 11), (10, 14), (10, 21), (10, 25), (11, 14), (12, 15), (12, 21), (13, 14), (14, 15), (14, 17), (14, 18), (14, 19), (14, 21), (14, 22), (14, 23), (14, 24), (14, 25), (14, 27), (15, 16), (15, 20), (15, 26), (21, 22), (21, 24)]
28
43
true
15
3
2
2
14
12
14
false
12
14
true
12
14
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 13), (0, 14), (0, 15), (0, 16), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (1, 12), (1, 13), (1, 14), (1, 15), (1, 16), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 14), (2, 15), (2, 16), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (4, 16), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 15), (6, 16), (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (8, 9), (8, 10), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (9, 16), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (10, 16), (11, 12), (11, 13), (11, 14), (11, 15), (11, 16), (12, 14), (12, 15), (12, 16), (13, 14), (13, 15), (13, 16), (14, 15), (14, 16), (15, 16)]
17
135
true
665
12
15
13
0,1,2,3,4,5,6,7,8,9,10,11,14,15,16
7
14
true
7
14
true
7
14
1
erdos
[(0, 1), (0, 5), (0, 6), (0, 7), (0, 8), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 9), (3, 4), (3, 10), (3, 11), (4, 10), (4, 12), (4, 13), (5, 6), (5, 16), (6, 7), (7, 8), (8, 11), (9, 15), (9, 20), (10, 13), (10, 18), (11, 18), (12, 13), (14, 15), (17, 19), (18, 19)]
21
31
true
10
1
4
5
0,6,16
19
0
false
19
0
true
19
0
4
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (2, 3), (2, 4), (2, 8), (3, 4), (3, 8), (3, 9), (4, 8), (5, 9), (6, 7)]
10
13
true
7
4
4
8
2,3,4
4
1
false
4
1
true
4
1
2
erdos
[(0, 1), (0, 2), (0, 4), (0, 6), (0, 8), (1, 2), (1, 4), (2, 6), (3, 5), (3, 11), (4, 11), (6, 8), (6, 9), (7, 10), (8, 9), (9, 10)]
12
16
true
5
7
1
1
0,2,4
6
4
false
6
4
true
6
4
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 13), (0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (0, 20), (0, 21), (0, 22), (0, 23), (0, 24), (0, 25), (0, 26), (0, 27), (0, 28), (0, 29), (0, 30), (0, 31), (0, 32), (0, 33), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (1, 12), (1, 13), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18), (1, 19), (1, 20), (1, 21), (1, 22), (1, 23), (1, 24), (1, 25), (1, 26), (1, 27), (1, 28), (1, 29), (1, 30), (1, 31), (1, 32), (1, 33), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 14), (2, 15), (2, 16), (2, 17), (2, 18), (2, 19), (2, 20), (2, 21), (2, 22), (2, 23), (2, 24), (2, 25), (2, 26), (2, 27), (2, 28), (2, 29), (2, 30), (2, 31), (2, 32), (2, 33), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (3, 18), (3, 19), (3, 20), (3, 21), (3, 22), (3, 23), (3, 24), (3, 25), (3, 26), (3, 27), (3, 28), (3, 29), (3, 30), (3, 31), (3, 32), (3, 33), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (4, 16), (4, 17), (4, 18), (4, 19), (4, 20), (4, 21), (4, 23), (4, 24), (4, 25), (4, 26), (4, 27), (4, 28), (4, 29), (4, 30), (4, 31), (4, 32), (4, 33), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (5, 17), (5, 18), (5, 19), (5, 20), (5, 21), (5, 22), (5, 23), (5, 24), (5, 25), (5, 26), (5, 27), (5, 28), (5, 29), (5, 30), (5, 31), (5, 32), (5, 33), (6, 7), (6, 9), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (6, 19), (6, 20), (6, 21), (6, 22), (6, 23), (6, 24), (6, 25), (6, 26), (6, 27), (6, 28), (6, 29), (6, 30), (6, 31), (6, 32), (6, 33), (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (7, 17), (7, 18), (7, 19), (7, 20), (7, 21), (7, 22), (7, 23), (7, 24), (7, 25), (7, 26), (7, 27), (7, 28), (7, 29), (7, 30), (7, 31), (7, 32), (7, 33), (8, 9), (8, 10), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (8, 19), (8, 20), (8, 21), (8, 22), (8, 23), (8, 24), (8, 25), (8, 26), (8, 27), (8, 28), (8, 29), (8, 30), (8, 31), (8, 32), (8, 33), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (9, 16), (9, 17), (9, 18), (9, 19), (9, 20), (9, 21), (9, 22), (9, 23), (9, 24), (9, 25), (9, 26), (9, 27), (9, 28), (9, 29), (9, 30), (9, 31), (9, 32), (9, 33), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (10, 16), (10, 17), (10, 18), (10, 19), (10, 20), (10, 21), (10, 22), (10, 23), (10, 24), (10, 25), (10, 26), (10, 27), (10, 28), (10, 29), (10, 30), (10, 31), (10, 32), (10, 33), (11, 12), (11, 13), (11, 14), (11, 15), (11, 16), (11, 17), (11, 18), (11, 19), (11, 20), (11, 21), (11, 22), (11, 23), (11, 24), (11, 25), (11, 26), (11, 27), (11, 28), (11, 29), (11, 30), (11, 31), (11, 32), (11, 33), (12, 13), (12, 14), (12, 15), (12, 16), (12, 17), (12, 18), (12, 19), (12, 20), (12, 21), (12, 22), (12, 24), (12, 25), (12, 26), (12, 27), (12, 28), (12, 29), (12, 30), (12, 31), (12, 32), (12, 33), (13, 14), (13, 15), (13, 16), (13, 17), (13, 18), (13, 19), (13, 20), (13, 21), (13, 22), (13, 23), (13, 24), (13, 25), (13, 26), (13, 27), (13, 28), (13, 29), (13, 30), (13, 31), (13, 32), (13, 33), (14, 15), (14, 16), (14, 17), (14, 18), (14, 19), (14, 20), (14, 21), (14, 22), (14, 23), (14, 24), (14, 25), (14, 26), (14, 27), (14, 28), (14, 29), (14, 30), (14, 31), (14, 32), (14, 33), (15, 16), (15, 17), (15, 18), (15, 19), (15, 20), (15, 21), (15, 22), (15, 23), (15, 24), (15, 25), (15, 26), (15, 27), (15, 28), (15, 29), (15, 30), (15, 31), (15, 32), (15, 33), (16, 17), (16, 18), (16, 19), (16, 20), (16, 21), (16, 22), (16, 23), (16, 24), (16, 25), (16, 26), (16, 27), (16, 28), (16, 29), (16, 30), (16, 31), (16, 32), (16, 33), (17, 18), (17, 19), (17, 20), (17, 21), (17, 22), (17, 23), (17, 24), (17, 25), (17, 26), (17, 27), (17, 28), (17, 29), (17, 30), (17, 31), (17, 32), (17, 33), (18, 19), (18, 20), (18, 21), (18, 22), (18, 23), (18, 24), (18, 25), (18, 26), (18, 27), (18, 28), (18, 29), (18, 30), (18, 31), (18, 32), (18, 33), (19, 20), (19, 21), (19, 22), (19, 23), (19, 24), (19, 25), (19, 26), (19, 27), (19, 28), (19, 29), (19, 30), (19, 31), (19, 32), (19, 33), (20, 21), (20, 22), (20, 23), (20, 24), (20, 25), (20, 26), (20, 27), (20, 28), (20, 29), (20, 30), (20, 31), (20, 32), (20, 33), (21, 22), (21, 23), (21, 24), (21, 25), (21, 26), (21, 27), (21, 28), (21, 29), (21, 30), (21, 31), (21, 32), (22, 23), (22, 24), (22, 25), (22, 26), (22, 27), (22, 28), (22, 29), (22, 30), (22, 31), (22, 32), (22, 33), (23, 24), (23, 25), (23, 26), (23, 27), (23, 28), (23, 29), (23, 30), (23, 31), (23, 32), (23, 33), (24, 25), (24, 26), (24, 27), (24, 28), (24, 29), (24, 30), (24, 31), (24, 32), (24, 33), (25, 26), (25, 27), (25, 28), (25, 29), (25, 30), (25, 31), (25, 32), (25, 33), (26, 27), (26, 28), (26, 29), (26, 30), (26, 31), (26, 32), (26, 33), (27, 28), (27, 29), (27, 30), (27, 31), (27, 32), (27, 33), (28, 29), (28, 30), (28, 31), (28, 32), (28, 33), (29, 30), (29, 31), (29, 32), (29, 33), (30, 31), (30, 32), (30, 33), (31, 32), (31, 33), (32, 33)]
34
557
true
5,856
31
33
6
0,1,2,3,4,5,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33
26
25
true
26
25
true
26
25
1
erdos
[(0, 1), (0, 22), (1, 5), (2, 10), (2, 22), (3, 4), (3, 6), (4, 7), (8, 9), (8, 12), (9, 15), (11, 14), (13, 14), (16, 17), (16, 20), (17, 18), (18, 19), (19, 21)]
23
18
false
0
7
1
19
18,21
10
1
false
10
1
true
10
1
4
erdos
[(0, 1), (0, 10), (1, 4), (2, 8), (2, 12), (3, 5), (3, 9), (3, 13), (4, 12), (5, 13), (6, 9), (6, 10), (7, 8), (7, 11), (8, 11), (9, 10)]
14
16
true
3
1
2
6
9,10
0
8
false
0
8
true
0
8
5
erdos
[(0, 5), (0, 8), (1, 6), (1, 7), (1, 19), (2, 3), (2, 10), (2, 12), (3, 5), (3, 10), (3, 15), (4, 17), (4, 19), (5, 7), (5, 15), (6, 10), (7, 18), (8, 14), (9, 12), (10, 12), (10, 15), (11, 15), (11, 18), (11, 19), (13, 16), (13, 17)]
20
26
true
4
1
3
5
0,3,7,15
14
3
false
14
3
true
14
3
4
erdos
[(0, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 4), (2, 6), (2, 8), (2, 9), (3, 4), (3, 6), (4, 5), (4, 6), (4, 11), (5, 11), (7, 8), (7, 10), (7, 15), (7, 16), (7, 17), (7, 19), (8, 15), (8, 21), (9, 11), (9, 21), (10, 16), (10, 17), (11, 12), (12, 13), (13, 14), (15, 18), (15, 19), (15, 20), (15, 21), (16, 17), (16, 19), (18, 19), (18, 20), (19, 20), (20, 21)]
22
40
true
19
13
2
13
12,14
12
18
false
12
18
true
12
18
5
erdos
[(0, 1), (0, 4), (0, 5), (0, 6), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 10), (2, 11), (3, 4), (3, 11), (4, 5), (5, 6), (6, 7), (7, 9), (7, 21), (8, 9), (9, 21), (10, 12), (10, 13), (10, 14), (10, 15), (12, 13), (12, 14), (12, 15), (13, 14), (14, 15), (14, 17), (15, 17), (16, 17), (18, 19), (18, 20), (20, 21)]
22
35
true
18
21
3
3
1,2,4,11
9
17
false
9
17
true
9
17
8
erdos
[(0, 1), (0, 5), (0, 6), (1, 3), (1, 4), (1, 5), (1, 6), (1, 8), (2, 6), (2, 7), (3, 4), (3, 8), (4, 8), (5, 6), (6, 7)]
9
15
true
9
7
2
4
1,3,8
8
3
true
8
3
true
8
3
1
erdos
[(0, 4), (0, 7), (0, 11), (1, 5), (2, 8), (3, 6), (3, 9), (3, 10), (4, 7), (4, 8), (4, 11), (5, 10), (6, 9), (6, 10), (7, 8), (7, 11), (9, 10)]
12
17
true
9
8
3
8
2,4,7
7
2
false
7
2
true
7
2
2
erdos
[(0, 15), (0, 17), (0, 18), (0, 20), (0, 23), (0, 24), (1, 15), (1, 16), (1, 17), (1, 18), (1, 19), (1, 20), (1, 22), (1, 23), (1, 24), (1, 25), (1, 26), (2, 15), (2, 17), (2, 19), (2, 23), (2, 24), (2, 25), (2, 26), (3, 15), (3, 16), (3, 17), (3, 18), (3, 19), (3, 21), (3, 22), (3, 23), (3, 24), (3, 25), (3, 26), (4, 15), (4, 16), (4, 17), (4, 19), (4, 21), (4, 22), (5, 15), (5, 16), (5, 17), (5, 18), (5, 19), (5, 22), (5, 23), (5, 24), (5, 25), (6, 15), (6, 23), (6, 24), (6, 25), (7, 15), (7, 16), (7, 17), (7, 18), (7, 19), (7, 20), (7, 21), (7, 24), (8, 15), (8, 17), (8, 20), (8, 21), (8, 23), (8, 25), (9, 15), (9, 16), (9, 17), (9, 18), (9, 19), (9, 22), (9, 23), (9, 24), (9, 25), (10, 15), (10, 16), (10, 17), (10, 19), (10, 20), (10, 22), (10, 24), (10, 25), (10, 26), (11, 15), (11, 16), (11, 18), (11, 20), (11, 21), (11, 23), (11, 25), (11, 26), (12, 15), (12, 16), (12, 17), (12, 19), (12, 21), (12, 23), (12, 24), (12, 25), (12, 26), (13, 15), (13, 16), (13, 17), (13, 18), (13, 19), (13, 20), (13, 21), (13, 23), (13, 24), (13, 25), (13, 26), (14, 15), (14, 16), (14, 17), (14, 18), (14, 19), (14, 20), (14, 21), (14, 22), (14, 23), (14, 24), (14, 26)]
27
125
true
0
4
6
21
3,4,7,8,11,12,13,14
9
0
false
9
0
true
9
0
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 12), (1, 2), (1, 3), (1, 12), (2, 3), (2, 12), (3, 12), (4, 25), (5, 9), (5, 11), (5, 18), (6, 7), (6, 8), (6, 10), (7, 8), (7, 10), (8, 10), (9, 11), (9, 18), (9, 27), (11, 18), (11, 21), (12, 19), (13, 14), (13, 15), (13, 16), (13, 17), (14, 15), (14, 16), (14, 17), (15, 16), (15, 17), (16, 17), (18, 21), (18, 29), (18, 30), (20, 22), (20, 23), (20, 24), (20, 25), (20, 26), (20, 28), (21, 29), (22, 23), (22, 24), (23, 24), (25, 26), (25, 28), (26, 28)]
31
52
true
38
6
3
0
1,2,3,12
10
6
true
10
6
true
10
6
1
erdos
[(0, 1), (0, 2), (1, 2), (1, 4), (2, 5), (2, 10), (3, 7), (3, 8), (3, 13), (4, 7), (4, 11), (5, 6), (5, 10), (6, 10), (7, 13), (7, 15), (8, 12), (8, 13), (8, 14), (9, 12), (11, 15), (12, 14), (13, 14)]
16
23
true
7
9
1
1
0,2,4
3
6
false
3
6
true
3
6
6
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]
4
6
true
4
3
3
1
0,2,3
0
2
true
0
2
true
0
2
1
erdos
[(0, 1), (0, 2), (0, 5), (0, 6), (1, 2), (1, 3), (1, 4), (1, 5), (2, 5), (2, 7), (3, 4), (3, 8), (4, 8), (4, 9), (4, 10), (5, 6), (5, 7), (5, 16), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (7, 16), (7, 25), (8, 10), (8, 30), (8, 31), (9, 10), (9, 11), (9, 12), (10, 12), (10, 30), (10, 31), (11, 12), (13, 14), (13, 15), (14, 15), (14, 17), (15, 18), (16, 17), (16, 19), (16, 20), (17, 19), (17, 20), (17, 22), (17, 27), (19, 20), (19, 21), (19, 22), (19, 23), (20, 21), (20, 22), (20, 24), (20, 25), (21, 22), (21, 23), (21, 26), (22, 23), (22, 27), (23, 26), (23, 27), (23, 29), (24, 25), (24, 28), (25, 28), (26, 29), (26, 32), (29, 32), (30, 31)]
33
71
true
45
27
3
22
17,19,20,21,23,27
14
17
true
14
17
true
14
17
1
erdos
[(0, 1), (0, 21), (0, 25), (1, 21), (1, 25), (2, 5), (2, 7), (2, 16), (2, 18), (2, 20), (3, 10), (4, 15), (4, 22), (5, 7), (5, 8), (5, 18), (5, 20), (5, 24), (6, 11), (6, 12), (7, 16), (7, 18), (8, 9), (8, 23), (8, 24), (9, 23), (9, 24), (10, 19), (11, 15), (13, 14), (13, 17), (13, 19), (14, 17), (14, 19), (16, 18), (16, 20), (17, 19), (17, 21), (18, 24), (19, 21), (20, 24), (23, 24)]
26
42
true
23
24
6
10
3,19
7
25
false
7
25
false
7
25
-1
erdos
[(0, 1), (0, 2), (0, 3), (0, 6), (0, 7), (0, 8), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 8), (2, 9), (3, 4), (3, 5), (3, 8), (4, 5), (6, 7), (6, 8), (6, 10), (6, 11), (6, 12), (7, 8), (7, 11), (7, 12), (8, 12), (9, 16), (10, 11), (11, 12), (13, 14), (13, 15), (13, 17), (14, 15), (14, 18), (15, 18), (16, 17)]
19
37
true
26
8
6
0
1,2,3,6,7,8
16
18
false
16
18
true
16
18
4
erdos
[(0, 2), (0, 4), (0, 6), (0, 8), (0, 9), (0, 10), (0, 13), (0, 14), (0, 16), (0, 18), (0, 20), (0, 21), (0, 22), (0, 23), (0, 24), (0, 26), (0, 27), (1, 2), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 16), (1, 17), (1, 19), (1, 20), (1, 21), (1, 24), (1, 25), (2, 4), (2, 6), (2, 7), (2, 8), (2, 9), (2, 13), (2, 16), (2, 17), (2, 20), (2, 21), (2, 23), (2, 24), (2, 25), (3, 10), (3, 11), (3, 12), (3, 14), (3, 15), (3, 18), (3, 22), (3, 26), (3, 27), (4, 6), (4, 8), (4, 9), (4, 10), (4, 13), (4, 14), (4, 16), (4, 18), (4, 20), (4, 21), (4, 22), (4, 23), (4, 24), (4, 26), (4, 27), (5, 7), (5, 12), (5, 17), (5, 19), (5, 25), (6, 7), (6, 8), (6, 9), (6, 13), (6, 16), (6, 17), (6, 20), (6, 21), (6, 23), (6, 24), (6, 25), (7, 8), (7, 9), (7, 16), (7, 17), (7, 19), (7, 20), (7, 21), (7, 24), (7, 25), (8, 9), (8, 13), (8, 16), (8, 17), (8, 20), (8, 21), (8, 23), (8, 24), (8, 25), (9, 13), (9, 16), (9, 17), (9, 20), (9, 21), (9, 23), (9, 24), (9, 25), (10, 11), (10, 13), (10, 14), (10, 15), (10, 18), (10, 22), (10, 23), (10, 26), (10, 27), (11, 12), (11, 14), (11, 15), (11, 18), (11, 22), (11, 26), (11, 27), (12, 15), (12, 19), (13, 14), (13, 16), (13, 18), (13, 20), (13, 21), (13, 22), (13, 23), (13, 24), (13, 26), (13, 27), (14, 15), (14, 18), (14, 22), (14, 23), (14, 26), (14, 27), (15, 18), (15, 22), (15, 26), (15, 27), (16, 17), (16, 20), (16, 21), (16, 23), (16, 24), (16, 25), (17, 19), (17, 20), (17, 21), (17, 24), (17, 25), (18, 22), (18, 23), (18, 26), (18, 27), (19, 25), (20, 21), (20, 23), (20, 24), (20, 25), (21, 23), (21, 24), (21, 25), (22, 23), (22, 26), (22, 27), (23, 24), (23, 26), (23, 27), (24, 25), (26, 27)]
28
178
true
584
19
6
25
1,2,5,6,7,8,9,16,17,19,20,21,24
25
23
false
25
23
true
25
23
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 6), (0, 7), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 5), (2, 8), (3, 5), (3, 6), (4, 6), (4, 7), (4, 9), (4, 10), (5, 8), (6, 7), (7, 9), (7, 10), (8, 31), (9, 10), (9, 24), (10, 24), (10, 25), (10, 26), (11, 12), (12, 15), (12, 18), (13, 22), (13, 23), (14, 18), (15, 16), (15, 17), (15, 18), (16, 17), (17, 18), (19, 20), (19, 21), (20, 21), (20, 22), (21, 22), (21, 23), (22, 23), (25, 26), (27, 28), (27, 29), (27, 30), (27, 31), (28, 29), (28, 30), (29, 31), (29, 32), (30, 31)]
33
57
true
31
20
3
22
13,20,21,23
7
19
false
7
19
false
7
19
-1
erdos
[(0, 11), (0, 13), (0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (1, 11), (1, 12), (1, 13), (1, 15), (1, 16), (1, 17), (2, 11), (2, 13), (2, 14), (2, 15), (2, 17), (3, 11), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (4, 17), (4, 18), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (5, 18), (6, 11), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (7, 11), (7, 12), (7, 15), (7, 16), (7, 17), (7, 18), (8, 11), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (9, 11), (9, 12), (9, 13), (9, 14), (9, 16), (9, 17), (9, 18), (10, 11), (10, 12), (10, 16), (10, 17)]
19
68
true
0
4
7
4
11,12,13,14,15,17,18
9
11
true
9
11
true
9
11
1
erdos
[(0, 4), (0, 6), (0, 13), (1, 12), (1, 23), (2, 3), (2, 25), (2, 29), (3, 7), (3, 19), (3, 30), (4, 33), (5, 7), (5, 12), (5, 27), (6, 27), (6, 31), (7, 17), (8, 28), (9, 14), (9, 30), (10, 22), (11, 17), (13, 21), (14, 15), (14, 24), (14, 32), (15, 20), (15, 25), (16, 30), (18, 29), (19, 20), (19, 21), (19, 30), (20, 28), (21, 32), (22, 32), (23, 29), (24, 33), (26, 31)]
34
40
true
1
1
2
23
1,29
17
25
false
17
25
true
17
25
4
erdos
[(0, 1), (0, 3), (0, 7), (0, 8), (1, 2), (1, 3), (1, 4), (1, 6), (1, 10), (2, 9), (3, 12), (4, 9), (4, 10), (5, 8), (5, 11), (6, 9), (6, 10), (7, 14), (7, 17), (8, 11), (9, 10), (11, 20), (12, 20), (13, 17), (14, 15), (14, 16), (15, 16), (15, 17), (15, 18), (17, 19), (18, 19), (18, 21), (19, 21)]
22
33
true
8
20
2
19
17,18,21
19
8
false
19
8
true
19
8
4
erdos
[(0, 10), (0, 12), (1, 14), (2, 3), (3, 12), (4, 7), (5, 20), (6, 8), (6, 9), (7, 14), (7, 16), (8, 18), (10, 17), (11, 13), (11, 20), (13, 19), (15, 17), (18, 19)]
21
18
false
0
12
2
9
6
0
10
true
0
10
true
0
10
1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 4), (1, 5), (1, 6), (2, 4), (3, 4), (3, 15), (4, 15), (5, 6), (5, 21), (5, 22), (5, 23), (5, 24), (6, 21), (6, 22), (6, 23), (6, 24), (7, 8), (7, 9), (7, 10), (8, 9), (8, 10), (8, 11), (9, 10), (9, 12), (9, 13), (9, 14), (10, 12), (10, 14), (11, 12), (11, 25), (12, 25), (13, 14), (13, 19), (13, 26), (13, 28), (13, 29), (14, 19), (14, 29), (15, 30), (16, 26), (16, 29), (17, 18), (17, 25), (18, 25), (18, 27), (19, 28), (19, 29), (20, 29), (21, 22), (21, 23), (23, 24), (26, 28), (26, 29), (27, 30), (28, 29)]
31
60
true
37
10
5
5
1,6,21,22,23,24
17
20
false
17
20
true
17
20
6
erdos
[(0, 7), (0, 10), (1, 7), (2, 21), (3, 17), (4, 22), (4, 24), (5, 11), (5, 17), (5, 18), (6, 21), (7, 8), (7, 9), (7, 10), (7, 20), (8, 9), (8, 10), (8, 20), (9, 10), (10, 20), (11, 12), (11, 14), (11, 17), (11, 18), (12, 18), (13, 15), (13, 16), (13, 22), (13, 23), (14, 17), (15, 16), (17, 18), (19, 22), (19, 24), (22, 23), (22, 24)]
25
36
true
18
17
5
14
11,17
21
22
false
21
22
false
21
22
-1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (6, 7), (6, 8), (6, 9), (6, 10), (7, 8), (7, 9), (7, 10), (8, 9), (8, 10), (9, 10)]
11
55
true
165
6
10
1
0,2,3,4,5,6,7,8,9,10
2
5
true
2
5
true
2
5
1
erdos
[(0, 1), (0, 6), (1, 5), (1, 6), (2, 3), (2, 4), (2, 9), (3, 4), (3, 9), (4, 5), (4, 9), (7, 8)]
10
12
true
5
2
3
5
1,4
5
1
true
5
1
true
5
1
1
erdos
[(0, 3), (0, 12), (0, 22), (1, 18), (1, 19), (2, 3), (2, 22), (3, 12), (4, 7), (4, 23), (5, 7), (5, 19), (5, 23), (6, 13), (8, 13), (8, 22), (9, 14), (10, 11), (10, 14), (10, 15), (11, 14), (11, 15), (12, 22), (15, 20), (16, 20), (17, 22), (18, 19), (18, 21)]
24
28
true
5
5
3
19
1,5,18
15
11
true
15
11
true
15
11
1
erdos
[(0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 9), (0, 11), (0, 13), (0, 14), (0, 15), (0, 17), (0, 18), (0, 19), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 12), (1, 13), (1, 14), (1, 15), (1, 16), (1, 17), (1, 19), (2, 4), (2, 5), (2, 7), (2, 8), (2, 9), (2, 11), (2, 12), (2, 14), (2, 17), (2, 18), (2, 19), (3, 4), (3, 5), (3, 7), (3, 9), (3, 11), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (3, 19), (4, 5), (4, 6), (4, 7), (4, 8), (4, 10), (4, 11), (4, 12), (4, 15), (4, 16), (4, 18), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (5, 12), (5, 14), (5, 15), (5, 16), (5, 17), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (6, 13), (6, 15), (6, 16), (6, 19), (7, 8), (7, 10), (7, 11), (7, 13), (7, 14), (7, 15), (7, 16), (7, 17), (7, 19), (8, 9), (8, 11), (8, 13), (8, 14), (8, 16), (9, 10), (9, 11), (9, 15), (9, 17), (9, 18), (9, 19), (10, 11), (10, 12), (10, 13), (10, 15), (10, 18), (11, 13), (11, 14), (11, 19), (12, 13), (12, 14), (12, 15), (12, 16), (12, 17), (12, 19), (13, 14), (13, 15), (13, 16), (13, 17), (13, 18), (14, 15), (14, 16), (14, 17), (14, 18), (15, 17), (16, 17), (16, 18), (16, 19), (17, 18), (17, 19), (18, 19)]
20
130
true
351
8
11
1
3,4,5,6,7,8,9,10,12,13,14,15,16,17,19
16
14
true
16
14
true
16
14
1
erdos
[(0, 2), (0, 4), (0, 7), (0, 8), (1, 3), (1, 4), (1, 5), (1, 6), (1, 9), (2, 7), (2, 8), (2, 10), (2, 12), (3, 4), (3, 5), (3, 6), (3, 16), (4, 5), (4, 6), (4, 12), (6, 7), (6, 12), (7, 10), (7, 12), (8, 10), (9, 13), (9, 14), (10, 12), (11, 16), (13, 14), (14, 15), (14, 17), (15, 17)]
18
33
true
18
3
5
0
2,4,7,8
10
0
false
10
0
true
10
0
2
erdos
[(0, 1), (1, 2), (2, 3), (4, 5), (5, 6), (6, 7), (8, 9), (8, 10), (9, 11), (11, 12), (12, 13), (14, 15)]
16
12
false
0
8
2
4
5
0
4
false
0
4
false
0
4
-1
erdos
[(0, 14), (0, 24), (0, 27), (0, 28), (1, 2), (1, 4), (1, 25), (3, 21), (3, 22), (5, 8), (5, 9), (5, 23), (6, 14), (6, 24), (6, 27), (6, 28), (7, 21), (7, 22), (8, 10), (8, 23), (9, 13), (9, 16), (9, 19), (9, 23), (10, 13), (10, 16), (10, 19), (10, 23), (11, 21), (11, 22), (12, 25), (12, 26), (14, 24), (14, 27), (14, 28), (14, 29), (15, 25), (15, 26), (17, 21), (17, 22), (18, 21), (18, 22), (20, 26), (21, 22), (24, 29), (27, 28), (27, 29), (28, 29)]
30
48
true
21
9
5
24
0,6,14,29
0
29
false
0
29
true
0
29
2
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (2, 4)]
5
5
true
1
4
1
3
0
0
3
true
0
3
true
0
3
1
erdos
[(0, 13), (0, 14), (0, 15), (1, 16), (1, 19), (2, 3), (3, 19), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (5, 6), (5, 7), (6, 7), (6, 8), (6, 9), (7, 8), (7, 9), (8, 9), (10, 11), (10, 12), (11, 12), (11, 13), (13, 14), (13, 15), (14, 15), (16, 17), (17, 18)]
20
29
true
18
6
5
15
0,13,14
2
1
false
2
1
true
2
1
3
erdos
[(0, 1), (0, 2), (1, 2), (1, 3), (2, 9), (3, 4), (4, 5), (5, 8), (5, 11), (5, 16), (6, 12), (6, 18), (7, 8), (8, 13), (8, 17), (9, 10), (10, 11), (11, 13), (11, 20), (13, 21), (14, 15), (15, 16), (18, 19), (19, 20)]
22
24
true
1
11
4
2
0,1,9
16
6
false
16
6
true
16
6
6
erdos
[(0, 4), (0, 9), (0, 10), (0, 16), (0, 17), (0, 18), (0, 19), (0, 20), (0, 21), (0, 23), (0, 24), (0, 26), (0, 27), (1, 4), (1, 8), (1, 10), (1, 12), (1, 14), (1, 20), (1, 24), (1, 30), (2, 3), (2, 4), (2, 7), (2, 8), (2, 11), (2, 12), (2, 17), (2, 18), (2, 22), (2, 23), (2, 25), (2, 27), (2, 29), (2, 30), (3, 5), (3, 7), (3, 10), (3, 11), (3, 12), (3, 13), (3, 14), (3, 15), (3, 18), (3, 23), (3, 25), (3, 26), (3, 30), (4, 6), (4, 7), (4, 8), (4, 12), (4, 13), (4, 14), (4, 25), (4, 27), (4, 30), (5, 8), (5, 10), (5, 11), (5, 13), (5, 16), (5, 18), (5, 19), (5, 21), (5, 23), (5, 27), (5, 28), (5, 30), (6, 7), (6, 8), (6, 10), (6, 17), (6, 22), (6, 23), (6, 24), (6, 30), (7, 8), (7, 11), (7, 12), (7, 13), (7, 15), (7, 17), (7, 19), (7, 23), (7, 27), (7, 28), (7, 30), (8, 12), (8, 18), (8, 19), (8, 27), (8, 28), (8, 29), (9, 12), (9, 15), (9, 21), (9, 24), (9, 30), (10, 14), (10, 18), (10, 20), (10, 22), (10, 24), (10, 28), (10, 30), (11, 13), (11, 14), (11, 15), (11, 18), (11, 19), (11, 20), (11, 23), (11, 24), (11, 26), (11, 27), (12, 18), (12, 21), (12, 23), (12, 30), (13, 16), (13, 20), (13, 22), (13, 28), (13, 30), (14, 16), (14, 20), (14, 22), (14, 24), (14, 25), (14, 30), (15, 18), (15, 19), (15, 20), (15, 21), (15, 25), (15, 26), (15, 27), (16, 20), (16, 21), (16, 23), (16, 24), (16, 25), (16, 29), (17, 20), (17, 21), (17, 25), (17, 28), (17, 29), (18, 19), (18, 20), (18, 22), (18, 26), (18, 27), (18, 28), (18, 30), (19, 24), (19, 25), (19, 30), (20, 23), (20, 24), (20, 25), (21, 25), (21, 26), (21, 27), (21, 28), (21, 30), (22, 25), (22, 30), (23, 24), (23, 25), (23, 30), (25, 26), (25, 27), (25, 28), (26, 27), (26, 29), (27, 28), (27, 29), (29, 30)]
31
180
true
270
26
9
27
0,2,4,5,7,8,11,15,18,21,25,26,28,29
6
16
false
6
16
true
6
16
2
erdos
[(0, 1), (0, 2), (0, 3), (1, 3), (2, 19), (3, 12), (4, 5), (4, 6), (4, 7), (6, 7), (8, 11), (8, 12), (9, 12), (9, 17), (10, 11), (10, 13), (10, 14), (10, 15), (10, 16), (11, 12), (11, 15), (12, 17), (13, 14), (13, 15), (13, 16), (13, 18), (14, 15), (14, 16), (14, 18), (16, 18)]
20
30
true
15
12
5
15
10,11,13,14
12
7
false
12
7
false
12
7
-1
erdos
[(0, 12), (0, 16), (0, 24), (1, 6), (1, 15), (1, 17), (1, 20), (1, 21), (1, 23), (1, 25), (2, 4), (2, 7), (2, 9), (2, 10), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (4, 7), (5, 6), (7, 19), (8, 27), (9, 10), (10, 16), (11, 14), (12, 13), (14, 15), (15, 26), (16, 17), (16, 19), (16, 21), (16, 24), (17, 19), (17, 21), (18, 19), (18, 28), (19, 21), (21, 22), (22, 25), (22, 26), (25, 26), (27, 28)]
29
43
true
13
16
6
9
2,10
3
27
false
3
27
true
3
27
6
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (3, 4), (4, 5), (5, 6), (5, 7), (6, 7)]
8
9
true
2
3
2
1
0,2
4
6
false
4
6
true
4
6
2
erdos
[(0, 5), (0, 6), (0, 10), (1, 3), (1, 6), (1, 13), (2, 4), (2, 9), (2, 10), (2, 14), (3, 10), (3, 11), (3, 13), (4, 7), (5, 12), (8, 10), (8, 11), (9, 14), (10, 12)]
15
19
true
2
6
2
5
0,12
4
6
false
4
6
true
4
6
4
erdos
[(0, 2), (0, 4), (0, 5), (1, 3), (1, 5), (2, 4)]
6
6
true
1
0
3
0
2,4,5
2
1
false
2
1
true
2
1
3
erdos
[(0, 1), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (0, 20), (1, 14), (1, 17), (1, 18), (1, 19), (1, 20), (2, 14), (2, 17), (2, 18), (2, 19), (2, 20), (3, 14), (3, 17), (3, 18), (3, 19), (3, 20), (4, 14), (4, 17), (4, 18), (4, 19), (4, 20), (5, 14), (5, 17), (5, 18), (5, 19), (5, 20), (6, 14), (6, 17), (6, 18), (6, 19), (6, 20), (7, 14), (7, 17), (7, 18), (7, 19), (7, 20), (8, 14), (8, 17), (8, 18), (8, 19), (8, 20), (9, 14), (9, 17), (9, 18), (9, 19), (9, 20), (10, 14), (10, 17), (10, 18), (10, 19), (10, 20), (11, 14), (11, 17), (11, 18), (11, 19), (11, 20), (12, 14), (12, 17), (12, 18), (12, 19), (12, 20), (13, 14), (13, 17), (13, 18), (13, 19), (13, 20), (14, 15), (14, 16), (14, 17), (14, 18), (14, 19), (14, 20), (15, 17), (15, 18), (15, 19), (15, 20), (16, 17), (16, 18), (16, 19), (16, 20), (17, 18), (17, 19), (17, 20), (18, 19), (18, 20), (19, 20)]
21
103
true
235
5
6
12
0,14,17,18,19,20
19
4
true
19
4
true
19
4
1