Datasets:
vstenby
/
erdos

Dataset card Data Studio Files
xet
Community
1
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, 4), (0, 7), (1, 13), (1, 27), (2, 16), (2, 27), (3, 14), (3, 24), (4, 25), (5, 9), (5, 26), (6, 16), (7, 13), (7, 25), (8, 10), (8, 12), (8, 20), (10, 24), (11, 15), (11, 19), (12, 21), (15, 23), (17, 19), (17, 22), (18, 22), (23, 26)]
28
26
true
0
21
1
8
10,12,20
27
13
false
27
13
true
27
13
2
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 9), (2, 10), (3, 11), (4, 5), (4, 9), (4, 12), (5, 7), (5, 8), (5, 9), (5, 10), (5, 13), (5, 14), (6, 7), (6, 8), (6, 15), (6, 16), (7, 8), (7, 10), (7, 16), (8, 13), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (8, 19), (9, 10), (9, 12), (10, 13), (11, 22), (11, 24), (11, 25), (12, 26), (13, 14), (13, 27), (13, 28), (14, 15), (14, 18), (14, 19), (14, 27), (15, 18), (15, 26), (17, 19), (17, 29), (18, 19), (20, 21), (20, 22), (20, 23), (20, 24), (21, 22), (21, 23), (22, 23), (22, 24), (23, 24), (23, 25), (24, 25), (26, 27), (28, 29), (29, 30)]
31
70
true
46
17
3
29
17,28,30
12
24
false
12
24
true
12
24
5
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)]
7
21
true
35
3
6
2
0,1,3,4,5,6
3
0
true
3
0
true
3
0
1
erdos
[(0, 1), (0, 3), (0, 7), (1, 5), (1, 6), (2, 4), (3, 5), (6, 7)]
8
8
true
0
3
2
2
4
6
1
true
6
1
true
6
1
1
erdos
[(0, 2), (0, 7), (0, 8), (0, 10), (1, 11), (1, 12), (1, 13), (2, 4), (2, 6), (2, 9), (2, 10), (3, 8), (4, 10), (5, 6), (6, 11), (7, 11), (7, 12), (7, 14), (8, 9), (11, 12), (11, 13), (11, 14), (12, 14)]
15
23
true
8
9
2
14
7,11,12
9
12
false
9
12
true
9
12
4
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (2, 3), (3, 4)]
5
6
true
2
4
1
2
0,1,3
0
3
true
0
3
true
0
3
1
erdos
[(0, 2), (0, 6), (1, 3), (2, 4), (3, 5), (5, 6)]
7
6
false
0
5
2
1
3
4
2
true
4
2
true
4
2
1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)]
7
21
true
35
2
6
1
0,2,3,4,5,6
2
3
true
2
3
true
2
3
1
erdos
[(0, 10), (0, 11), (0, 12), (0, 13), (0, 15), (0, 19), (0, 20), (1, 10), (1, 11), (1, 13), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18), (1, 19), (1, 20), (2, 10), (2, 12), (2, 14), (2, 15), (2, 16), (2, 17), (2, 18), (2, 19), (3, 10), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (3, 18), (3, 19), (3, 20), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (4, 16), (4, 17), (4, 18), (4, 19), (4, 20), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (5, 17), (5, 19), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (6, 19), (7, 10), (7, 12), (7, 13), (7, 15), (7, 17), (7, 18), (7, 19), (7, 20), (8, 10), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (8, 19), (8, 20), (9, 10), (9, 11), (9, 13), (9, 14), (9, 15), (9, 16), (9, 18), (9, 20)]
21
92
true
0
10
10
5
10,11,12,13,14,15,16,17,19
12
14
false
12
14
true
12
14
2
erdos
[(0, 6), (1, 2), (2, 3), (3, 6), (4, 6), (5, 6)]
7
6
false
0
0
1
6
0,3,4,5
4
1
false
4
1
true
4
1
4
erdos
[(0, 22), (1, 15), (1, 20), (2, 5), (2, 17), (2, 23), (3, 6), (3, 13), (4, 6), (4, 13), (5, 13), (7, 10), (7, 11), (7, 14), (8, 21), (9, 12), (9, 16), (11, 19), (13, 23), (14, 15), (16, 22), (18, 19), (18, 20), (21, 22)]
24
24
true
0
4
2
16
9,22
18
16
false
18
16
false
18
16
-1
erdos
[(0, 1), (0, 2), (0, 7), (1, 2), (1, 4), (2, 4), (2, 7), (3, 5), (3, 6), (4, 7), (5, 6), (5, 8), (7, 8)]
9
13
true
5
7
4
2
0,1,4,7
7
4
true
7
4
true
7
4
1
erdos
[(0, 1), (0, 3), (1, 2), (1, 3), (2, 3)]
4
5
true
2
3
3
2
1,3
0
3
true
0
3
true
0
3
1
erdos
[(0, 1), (0, 3), (0, 6), (1, 3), (2, 4), (2, 5), (3, 6), (3, 7), (4, 5), (4, 25), (5, 25), (5, 26), (6, 23), (7, 22), (7, 23), (7, 24), (8, 9), (9, 10), (10, 14), (10, 20), (11, 12), (11, 18), (13, 14), (13, 20), (13, 21), (14, 20), (14, 21), (15, 16), (15, 17), (16, 17), (16, 18), (19, 25), (19, 26), (20, 21), (22, 23), (22, 24), (23, 24), (25, 26)]
27
38
true
16
26
3
1
0,3
6
9
false
6
9
false
6
9
-1
erdos
[(0, 26), (0, 28), (1, 26), (1, 27), (1, 28), (2, 3), (3, 4), (5, 22), (5, 24), (6, 7), (6, 8), (7, 8), (7, 9), (8, 9), (10, 11), (10, 12), (10, 13), (11, 12), (11, 13), (12, 13), (13, 14), (15, 16), (15, 17), (15, 18), (15, 19), (16, 17), (16, 18), (17, 18), (17, 19), (20, 21), (20, 23), (21, 23), (22, 24), (24, 25), (26, 27), (26, 28), (27, 28)]
29
37
true
18
21
2
22
5,24
21
14
false
21
14
false
21
14
-1
erdos
[(0, 3), (0, 10), (1, 2), (1, 10), (2, 9), (4, 7), (4, 8), (5, 6), (5, 7), (6, 11), (8, 9), (8, 12), (9, 11)]
13
13
true
0
9
3
5
6,7
12
4
false
12
4
true
12
4
2
erdos
[(0, 3), (1, 4), (1, 20), (2, 4), (2, 5), (3, 10), (4, 5), (4, 21), (5, 21), (6, 7), (6, 8), (6, 14), (7, 8), (7, 14), (7, 18), (8, 18), (9, 13), (9, 16), (10, 13), (10, 14), (11, 12), (11, 13), (12, 13), (12, 15), (13, 15), (14, 18), (15, 16), (17, 23), (18, 19), (20, 22), (22, 23)]
24
31
true
8
4
4
9
13,16
2
20
false
2
20
true
2
20
3
erdos
[(0, 7), (0, 8), (0, 17), (1, 3), (1, 9), (1, 14), (1, 17), (1, 18), (2, 13), (2, 14), (2, 25), (3, 7), (3, 16), (3, 24), (4, 14), (4, 19), (5, 8), (5, 9), (5, 12), (5, 21), (6, 17), (7, 19), (8, 10), (8, 24), (11, 12), (11, 16), (12, 13), (12, 25), (13, 19), (13, 24), (13, 25), (15, 20), (15, 22), (18, 22), (18, 23), (20, 21), (21, 25)]
26
37
true
2
23
1
9
1,5
24
15
false
24
15
true
24
15
5
erdos
[(0, 3), (0, 4), (0, 5), (0, 6), (0, 10), (1, 3), (1, 8), (1, 9), (2, 4), (3, 4), (3, 8), (4, 6), (4, 7), (5, 6), (5, 8), (6, 9), (6, 10), (6, 11), (7, 9), (8, 11), (10, 12)]
13
21
true
5
0
5
10
0,6,12
10
12
true
10
12
true
10
12
1
erdos
[(0, 4), (0, 6), (1, 2), (1, 5), (1, 13), (1, 15), (2, 5), (2, 6), (2, 15), (3, 10), (3, 12), (4, 6), (5, 13), (5, 15), (7, 8), (7, 14), (8, 12), (9, 10), (9, 11), (9, 12), (10, 11), (10, 12), (11, 12), (13, 15)]
16
24
true
13
5
4
13
1,5,15
9
2
false
9
2
false
9
2
-1
erdos
[(0, 1), (0, 4), (1, 4), (2, 3), (2, 5), (4, 5)]
6
6
true
1
5
2
0
1,4
0
1
true
0
1
true
0
1
1
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, 28), (4, 29), (5, 6), (5, 7), (5, 18), (6, 7), (6, 17), (6, 18), (7, 15), (7, 17), (7, 18), (7, 30), (8, 25), (8, 26), (8, 27), (8, 30), (8, 31), (9, 10), (9, 11), (9, 12), (9, 13), (9, 16), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (11, 12), (11, 13), (11, 16), (12, 13), (12, 14), (12, 16), (13, 14), (13, 15), (13, 17), (14, 15), (14, 17), (14, 18), (15, 17), (15, 18), (17, 18), (18, 30), (19, 20), (19, 21), (19, 22), (19, 23), (20, 22), (20, 24), (20, 25), (21, 22), (21, 23), (22, 24), (22, 26), (24, 25), (24, 26), (24, 27), (25, 26), (25, 27), (26, 27), (27, 30), (27, 31), (28, 29), (30, 31), (30, 32), (31, 32)]
33
82
true
69
7
7
28
4,29
6
20
false
6
20
true
6
20
5
erdos
[(0, 1), (0, 2), (1, 2), (1, 3), (2, 3), (3, 4)]
5
6
true
2
4
1
3
1,2,4
4
1
false
4
1
true
4
1
2
erdos
[(0, 2), (0, 4), (0, 5), (0, 6), (0, 8), (0, 9), (0, 10), (0, 11), (0, 12), (0, 13), (0, 14), (0, 15), (0, 17), (1, 2), (1, 3), (1, 5), (1, 6), (1, 7), (1, 8), (1, 12), (1, 13), (1, 14), (1, 17), (2, 3), (2, 4), (2, 5), (2, 6), (2, 9), (2, 11), (2, 12), (2, 14), (2, 15), (2, 16), (2, 17), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11), (3, 12), (3, 13), (3, 15), (3, 16), (3, 17), (4, 8), (4, 9), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 17), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (5, 17), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (6, 12), (6, 13), (6, 15), (6, 16), (6, 17), (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 17), (8, 9), (8, 10), (8, 11), (8, 12), (8, 13), (8, 15), (8, 16), (8, 17), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (9, 16), (9, 17), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (10, 16), (10, 17), (11, 12), (11, 13), (11, 14), (11, 16), (11, 17), (12, 13), (12, 14), (12, 15), (12, 17), (13, 14), (13, 16), (13, 17), (14, 17), (15, 16), (15, 17)]
18
123
true
433
16
10
7
1,3,5,6,8,9,10,11,12,13,14,15,17
16
14
false
16
14
true
16
14
2
erdos
[(0, 6), (0, 15), (0, 25), (1, 3), (1, 28), (2, 6), (3, 20), (3, 22), (4, 22), (4, 27), (5, 13), (5, 20), (6, 18), (6, 21), (7, 16), (8, 15), (8, 26), (9, 10), (10, 11), (10, 20), (10, 28), (11, 19), (11, 28), (12, 26), (12, 29), (13, 19), (14, 27), (16, 23), (17, 19), (17, 24), (18, 20), (19, 24), (21, 24), (23, 25)]
30
34
true
2
14
1
28
1,10,11
12
13
false
12
13
true
12
13
9
erdos
[(0, 1), (0, 3), (0, 4), (1, 3), (1, 5), (2, 11), (2, 15), (2, 19), (3, 4), (3, 5), (3, 6), (5, 6), (5, 14), (5, 17), (5, 19), (6, 11), (6, 19), (7, 8), (7, 9), (8, 10), (9, 10), (11, 19), (12, 13), (12, 15), (14, 16), (14, 17), (14, 18), (15, 19), (16, 20), (17, 19)]
21
30
true
10
3
5
17
5,14,19
13
11
false
13
11
true
13
11
4
erdos
[(0, 1), (0, 2), (3, 4), (4, 5), (5, 6), (6, 7), (8, 9), (9, 10), (10, 11), (11, 12), (13, 15), (14, 15), (16, 17), (16, 18), (17, 24), (19, 20), (19, 21), (21, 22), (22, 23), (24, 25), (26, 27), (27, 28), (28, 29), (29, 30)]
31
24
false
0
14
1
3
4
0
13
false
0
13
false
0
13
-1
erdos
[(0, 28), (1, 2), (2, 3), (3, 4), (3, 5), (4, 10), (4, 11), (5, 17), (6, 13), (6, 14), (7, 13), (8, 12), (8, 27), (9, 27), (9, 29), (11, 23), (12, 15), (12, 16), (12, 27), (14, 26), (15, 28), (17, 22), (18, 21), (19, 20), (19, 26), (19, 30), (20, 26), (20, 30), (21, 25), (22, 24), (22, 25), (24, 25), (26, 30), (27, 29)]
31
34
true
7
9
2
19
20,26,30
16
15
false
16
15
true
16
15
2
erdos
[(0, 1), (0, 3), (0, 22), (1, 3), (1, 22), (1, 25), (2, 4), (2, 5), (2, 15), (2, 16), (3, 22), (3, 24), (3, 25), (4, 5), (4, 6), (4, 7), (5, 6), (5, 15), (5, 16), (6, 7), (7, 8), (7, 9), (8, 9), (8, 18), (10, 12), (10, 13), (10, 14), (11, 17), (13, 14), (13, 19), (13, 20), (13, 21), (14, 19), (15, 16), (19, 20), (19, 21), (20, 21), (22, 23), (22, 24), (22, 25), (23, 24), (23, 25), (24, 25)]
26
43
true
27
18
1
11
17
23
6
false
23
6
false
23
6
-1
erdos
[(0, 16), (1, 5), (1, 16), (1, 21), (2, 6), (2, 8), (3, 4), (3, 14), (3, 17), (3, 19), (4, 17), (4, 19), (4, 20), (5, 8), (5, 9), (5, 21), (7, 13), (7, 18), (8, 9), (10, 11), (10, 14), (10, 17), (10, 19), (12, 15), (12, 17), (12, 19), (12, 20), (13, 18), (14, 17), (15, 17), (15, 19), (15, 20), (16, 21), (17, 19), (17, 20), (19, 20)]
22
36
true
23
18
2
4
3,17,19,20
12
14
false
12
14
true
12
14
2
erdos
[(0, 1), (0, 2), (0, 14), (0, 15), (1, 2), (1, 14), (2, 14), (3, 10), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 13), (5, 11), (6, 7), (6, 8), (6, 12), (6, 13), (7, 8), (7, 9), (7, 10), (8, 9), (8, 10), (9, 10), (11, 15), (12, 13), (14, 15)]
16
28
true
20
0
4
3
10
6
5
false
6
5
false
6
5
-1
erdos
[(0, 1), (0, 2), (0, 7), (1, 7), (3, 4), (4, 5), (4, 6), (5, 6)]
8
8
true
2
5
2
7
0,1
6
2
false
6
2
false
6
2
-1
erdos
[(0, 4), (0, 8), (1, 2), (1, 19), (2, 8), (3, 4), (3, 9), (5, 13), (6, 14), (6, 17), (7, 16), (8, 16), (10, 18), (11, 13), (11, 15), (12, 15), (12, 17), (13, 14), (13, 17), (14, 17), (14, 18), (16, 19)]
20
22
true
2
12
2
2
1,8
2
4
false
2
4
true
2
4
3
erdos
[(0, 2), (1, 4), (1, 5), (1, 6), (2, 3), (3, 4), (4, 5), (4, 6), (4, 7), (5, 6), (5, 7), (6, 7)]
8
12
true
7
3
2
5
1,4,6,7
6
4
true
6
4
true
6
4
1
erdos
[(0, 1), (0, 2), (1, 2), (1, 4), (1, 5), (1, 6), (2, 5), (2, 8), (3, 7), (3, 14), (3, 31), (4, 5), (4, 6), (4, 8), (4, 22), (4, 23), (4, 24), (4, 25), (5, 6), (5, 8), (6, 23), (6, 24), (6, 25), (7, 14), (7, 15), (7, 31), (8, 23), (9, 10), (9, 11), (9, 12), (9, 13), (10, 11), (10, 12), (10, 13), (10, 16), (11, 12), (12, 13), (12, 16), (13, 16), (14, 31), (15, 30), (15, 31), (17, 18), (17, 19), (17, 20), (18, 19), (18, 20), (18, 21), (19, 20), (19, 21), (22, 24), (22, 25), (22, 26), (22, 27), (22, 28), (23, 24), (24, 25), (24, 26), (25, 26), (25, 27), (26, 27), (26, 28), (27, 28), (27, 29), (28, 29), (29, 30), (30, 31)]
32
67
true
50
1
5
30
15,29,31
26
20
false
26
20
false
26
20
-1
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4)]
6
9
true
4
5
2
0
1,2,3
5
0
false
5
0
true
5
0
2
erdos
[(0, 1), (0, 5), (0, 10), (0, 13), (1, 3), (2, 10), (2, 13), (2, 17), (3, 4), (4, 19), (5, 12), (6, 8), (6, 14), (7, 11), (7, 14), (7, 15), (9, 10), (10, 11), (10, 16), (12, 18), (15, 20), (16, 17), (17, 18)]
21
23
true
0
3
2
10
0,2,9,11,16
0
10
true
0
10
true
0
10
1
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 4), (4, 5)]
6
7
true
2
5
1
4
2,5
4
3
false
4
3
true
4
3
3
erdos
[(0, 2), (0, 3), (0, 5), (0, 6), (0, 11), (1, 2), (1, 7), (1, 8), (1, 11), (2, 4), (2, 5), (2, 7), (2, 9), (3, 7), (4, 5), (4, 8), (4, 9), (4, 10), (5, 10), (5, 11), (7, 11), (10, 11)]
12
22
true
8
9
2
7
1,2,3,11
9
2
true
9
2
true
9
2
1
erdos
[(0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (3, 5)]
6
6
true
1
3
3
5
3
2
0
true
2
0
true
2
0
1
erdos
[(0, 9), (0, 10), (0, 11), (0, 12), (0, 13), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (0, 20), (1, 9), (1, 10), (1, 12), (1, 13), (1, 15), (1, 16), (1, 17), (1, 19), (1, 20), (1, 21), (2, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 14), (2, 17), (2, 18), (2, 19), (2, 20), (2, 21), (3, 9), (3, 10), (3, 11), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (3, 19), (3, 20), (3, 21), (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), (5, 9), (5, 10), (5, 11), (5, 12), (5, 14), (5, 15), (5, 16), (5, 17), (5, 18), (5, 19), (5, 20), (5, 21), (6, 9), (6, 10), (6, 11), (6, 12), (6, 15), (6, 16), (6, 17), (6, 18), (6, 19), (6, 20), (6, 21), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (7, 17), (7, 19), (7, 20), (7, 21), (8, 9), (8, 10), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (8, 20), (8, 21)]
22
104
true
0
16
8
7
9,10,11,12,13,14,15,16,17,19,20,21
6
18
true
6
18
true
6
18
1
erdos
[(0, 4), (0, 10), (1, 2), (1, 7), (2, 15), (3, 5), (3, 8), (4, 8), (5, 9), (6, 11), (6, 13), (11, 12), (12, 14), (13, 15), (14, 16)]
17
15
false
0
12
2
1
2,7
8
6
false
8
6
false
8
6
-1
erdos
[(0, 3), (0, 4), (0, 8), (1, 7), (1, 8), (2, 7), (5, 6)]
9
7
false
0
6
1
6
5
8
7
false
8
7
true
8
7
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (1, 2), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (3, 4), (3, 6), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 17), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 15), (4, 17), (4, 18), (4, 19), (4, 20), (5, 6), (5, 7), (5, 9), (5, 11), (6, 7), (6, 8), (6, 12), (6, 16), (6, 17), (6, 18), (7, 8), (7, 9), (7, 10), (7, 11), (7, 17), (7, 18), (7, 21), (8, 9), (8, 10), (8, 11), (8, 17), (8, 18), (8, 19), (8, 20), (8, 21), (9, 10), (9, 23), (10, 11), (10, 18), (10, 19), (10, 20), (10, 21), (10, 22), (10, 23), (10, 24), (11, 18), (11, 21), (11, 23), (11, 25), (12, 13), (12, 14), (12, 15), (12, 16), (12, 17), (13, 14), (13, 15), (13, 16), (13, 17), (13, 27), (13, 28), (13, 29), (14, 15), (14, 16), (14, 26), (14, 27), (14, 28), (15, 16), (15, 17), (15, 27), (15, 28), (15, 29), (16, 17), (16, 29), (17, 18), (17, 19), (17, 29), (17, 30), (18, 19), (18, 20), (18, 21), (18, 22), (18, 29), (18, 30), (18, 31), (19, 20), (19, 21), (19, 22), (19, 29), (19, 30), (19, 31), (20, 21), (20, 22), (20, 23), (20, 24), (20, 30), (20, 31), (21, 22), (21, 23), (21, 24), (21, 25), (21, 30), (21, 31), (22, 23), (22, 24), (22, 25), (22, 30), (22, 31), (23, 24), (24, 25), (24, 31), (25, 31), (26, 27), (26, 32), (27, 28), (27, 29), (27, 32), (28, 29), (28, 32), (29, 30), (29, 32), (30, 31)]
33
153
true
276
19
11
5
0,1,2,6,7,9,11
15
0
false
15
0
true
15
0
2
erdos
[(0, 2), (1, 3), (1, 7), (4, 5), (4, 6), (4, 8), (5, 6), (5, 8), (5, 9), (6, 8), (7, 9)]
10
11
true
4
8
3
8
4,5,6
4
1
false
4
1
true
4
1
4
erdos
[(0, 1), (0, 6), (1, 2), (3, 5), (3, 6), (3, 9), (4, 7), (4, 8), (5, 9), (7, 9)]
10
10
true
1
6
2
2
1
9
7
true
9
7
true
9
7
1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 6), (0, 7), (0, 8), (0, 9), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (3, 6), (3, 7), (3, 9), (4, 6), (5, 9), (6, 7), (6, 8), (6, 10), (7, 8), (7, 10), (7, 11), (8, 10), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (9, 19), (10, 11), (10, 15), (11, 15), (12, 13), (12, 16), (12, 17), (12, 18), (13, 14), (13, 16), (13, 17), (14, 15), (14, 20), (15, 20), (16, 17), (16, 18), (17, 18)]
21
52
true
47
8
9
10
6,7,8,11,15
12
7
false
12
7
true
12
7
2
erdos
[(0, 1), (0, 4), (1, 2), (2, 3)]
5
4
false
0
4
1
1
0,2
2
0
false
2
0
true
2
0
2
erdos
[(0, 9), (0, 10), (0, 12), (0, 13), (0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (1, 9), (1, 10), (1, 11), (1, 13), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18), (2, 9), (2, 10), (2, 12), (2, 13), (2, 14), (2, 15), (2, 16), (2, 17), (2, 18), (3, 9), (3, 10), (3, 12), (3, 13), (3, 14), (3, 15), (3, 16), (3, 18), (4, 9), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (4, 16), (4, 17), (4, 18), (5, 9), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (5, 16), (5, 17), (5, 18), (6, 9), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (7, 17), (7, 18), (8, 9), (8, 10), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18)]
19
81
true
0
10
8
14
0,1,2,3,4,5,6,7,8
5
15
true
5
15
true
5
15
1
erdos
[(0, 4), (0, 10), (0, 17), (1, 2), (1, 6), (1, 7), (1, 10), (1, 14), (1, 18), (2, 3), (2, 5), (2, 6), (2, 12), (2, 13), (2, 16), (2, 17), (2, 18), (2, 20), (2, 21), (3, 6), (3, 12), (3, 18), (3, 21), (4, 17), (5, 6), (5, 7), (5, 10), (5, 11), (5, 12), (5, 16), (6, 7), (6, 12), (6, 14), (6, 15), (6, 18), (7, 8), (7, 10), (7, 11), (7, 15), (7, 18), (8, 18), (9, 17), (11, 12), (11, 15), (11, 17), (11, 18), (12, 14), (12, 17), (12, 18), (12, 20), (13, 17), (13, 19), (15, 17), (16, 18), (16, 19), (17, 22), (20, 21)]
23
57
true
41
22
1
4
0,17
4
3
false
4
3
true
4
3
3
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (1, 20), (1, 21), (2, 3), (2, 20), (3, 21), (4, 5), (4, 6), (5, 6), (6, 7), (7, 14), (7, 16), (7, 17), (8, 12), (8, 13), (9, 10), (9, 12), (9, 13), (11, 12), (12, 13), (14, 16), (14, 18), (14, 19), (15, 16), (15, 17), (16, 17), (16, 18), (18, 19), (20, 21)]
22
33
true
15
0
3
20
1,2,21
4
17
false
4
17
true
4
17
3
erdos
[(0, 8), (0, 11), (0, 15), (1, 2), (1, 3), (1, 5), (2, 5), (2, 15), (3, 5), (4, 6), (6, 7), (6, 18), (7, 18), (8, 11), (8, 15), (9, 13), (9, 14), (9, 19), (10, 19), (10, 21), (10, 22), (11, 15), (12, 16), (12, 17), (13, 14), (13, 26), (14, 19), (14, 22), (16, 17), (17, 20), (19, 22), (20, 23), (20, 24), (20, 25), (21, 22), (23, 24), (24, 25)]
27
37
true
15
15
4
7
6,18
18
21
false
18
21
false
18
21
-1
erdos
[(0, 2), (0, 16), (0, 17), (0, 20), (0, 21), (1, 2), (1, 12), (1, 15), (2, 12), (2, 20), (2, 21), (3, 6), (3, 7), (3, 8), (3, 9), (4, 5), (4, 19), (7, 8), (7, 9), (8, 9), (9, 18), (10, 11), (10, 13), (10, 14), (10, 18), (11, 13), (11, 14), (11, 18), (12, 15), (13, 14), (13, 18), (16, 17), (16, 21), (17, 21), (20, 21)]
22
35
true
21
15
2
8
3,7,9
3
14
false
3
14
true
3
14
4
erdos
[(0, 6), (0, 18), (0, 27), (0, 30), (1, 13), (1, 15), (1, 17), (1, 19), (1, 28), (1, 29), (1, 31), (2, 3), (2, 4), (2, 5), (2, 7), (2, 10), (2, 22), (3, 5), (3, 7), (3, 9), (3, 10), (3, 12), (3, 22), (3, 31), (4, 7), (4, 22), (5, 7), (5, 9), (5, 10), (5, 22), (6, 18), (6, 20), (6, 27), (6, 30), (7, 9), (7, 10), (7, 22), (8, 11), (8, 25), (8, 26), (9, 12), (9, 22), (9, 24), (10, 22), (11, 25), (11, 26), (12, 22), (12, 24), (12, 31), (13, 15), (13, 19), (13, 24), (13, 28), (13, 29), (13, 31), (14, 18), (14, 23), (14, 30), (15, 17), (15, 19), (15, 28), (15, 29), (15, 31), (16, 21), (17, 28), (17, 29), (17, 31), (18, 20), (18, 27), (18, 30), (19, 28), (19, 29), (20, 24), (20, 27), (21, 26), (22, 31), (25, 26), (27, 30), (28, 29), (28, 31), (29, 31)]
32
81
true
94
21
2
15
1,13,17,19,28,29,31
23
27
false
23
27
true
23
27
3
erdos
[(0, 2), (1, 16), (1, 31), (2, 13), (3, 26), (4, 5), (4, 6), (5, 6), (6, 9), (7, 8), (7, 28), (8, 16), (9, 13), (10, 11), (11, 12), (12, 24), (14, 15), (14, 25), (16, 31), (17, 18), (17, 19), (18, 19), (19, 30), (20, 21), (20, 27), (21, 22), (21, 23), (22, 23), (22, 24), (23, 24), (26, 30), (28, 29)]
32
32
true
5
10
1
15
14
28
31
false
28
31
true
28
31
4
erdos
[(0, 1), (0, 9), (1, 9), (2, 4), (2, 5), (2, 6), (2, 7), (2, 10), (3, 4), (3, 7), (3, 10), (4, 6), (4, 7), (4, 10), (5, 6), (5, 8), (6, 7), (6, 8), (6, 10), (7, 10)]
11
20
true
16
2
5
8
5,6
0
4
false
0
4
false
0
4
-1
erdos
[(0, 5), (0, 10), (0, 13), (0, 16), (0, 17), (1, 6), (2, 3), (3, 17), (3, 19), (4, 5), (5, 9), (6, 8), (7, 12), (7, 14), (8, 13), (8, 18), (11, 13), (12, 14), (12, 15), (13, 15), (18, 19)]
20
21
true
1
11
1
15
12,13
13
14
false
13
14
true
13
14
3
erdos
[(0, 5), (0, 6), (1, 2), (1, 3), (2, 5), (4, 6)]
7
6
false
0
2
2
1
2,3
6
5
false
6
5
true
6
5
2
erdos
[(0, 8), (0, 9), (0, 10), (0, 31), (1, 2), (1, 24), (2, 24), (3, 4), (3, 15), (3, 22), (4, 22), (5, 11), (5, 14), (6, 11), (7, 14), (7, 23), (8, 9), (8, 10), (8, 19), (9, 10), (9, 29), (9, 31), (10, 31), (12, 16), (12, 17), (12, 26), (13, 16), (15, 22), (17, 26), (18, 20), (18, 29), (20, 29), (21, 24), (21, 25), (21, 27), (21, 28), (22, 30), (25, 27), (25, 28), (26, 30), (27, 28), (29, 31)]
32
42
true
17
10
4
12
16,17,26
28
13
false
28
13
false
28
13
-1
erdos
[(0, 2), (0, 4), (1, 3), (1, 7), (1, 8), (2, 4), (2, 5), (2, 10), (2, 11), (3, 7), (3, 8), (3, 9), (3, 10), (4, 5), (4, 6), (5, 6), (5, 11), (6, 11), (7, 8), (7, 9), (7, 10), (8, 9), (8, 10), (9, 10), (11, 12)]
13
25
true
18
11
4
4
0,2,5,6
7
1
true
7
1
true
7
1
1
erdos
[(0, 2), (1, 6), (1, 11), (2, 4), (3, 5), (3, 19), (4, 16), (5, 13), (7, 8), (7, 17), (8, 9), (9, 18), (10, 16), (11, 12), (11, 14), (12, 14), (13, 15), (13, 20), (19, 20)]
21
19
true
1
3
2
4
2,16
0
8
false
0
8
false
0
8
-1
erdos
[(0, 1), (0, 9), (0, 10), (0, 14), (0, 15), (0, 17), (1, 7), (1, 9), (1, 10), (1, 11), (1, 14), (1, 15), (1, 17), (2, 5), (2, 8), (2, 12), (3, 4), (3, 5), (3, 6), (3, 8), (3, 12), (3, 16), (4, 5), (4, 6), (4, 8), (4, 12), (4, 16), (5, 6), (5, 8), (5, 12), (5, 16), (5, 18), (6, 8), (6, 12), (6, 16), (6, 18), (7, 9), (7, 10), (7, 13), (7, 15), (8, 12), (8, 16), (9, 10), (9, 14), (9, 15), (10, 11), (10, 14), (10, 15), (10, 17), (11, 13), (11, 14), (11, 17), (14, 15), (14, 17)]
19
54
true
72
1
8
10
0,1,7,9,11,14,15,17
4
15
false
4
15
false
4
15
-1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)]
7
21
true
35
6
6
4
0,1,2,3,5,6
2
5
true
2
5
true
2
5
1
erdos
[(0, 30), (1, 2), (2, 3), (3, 4), (5, 6), (5, 7), (6, 8), (9, 10), (10, 11), (10, 13), (11, 12), (13, 14), (15, 16), (15, 17), (18, 29), (19, 20), (20, 21), (21, 22), (22, 23), (24, 25), (24, 27), (25, 26), (27, 28), (30, 31)]
32
24
false
0
16
1
0
30
18
19
false
18
19
false
18
19
-1
erdos
[(0, 13), (1, 2), (1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 7), (3, 11), (4, 5), (4, 6), (4, 7), (4, 11), (5, 6), (7, 11), (8, 9), (8, 10), (9, 10), (11, 13), (11, 19), (12, 13), (12, 14), (12, 15), (12, 19), (13, 14), (13, 19), (14, 19), (15, 16), (16, 19), (16, 20), (17, 18), (17, 19), (18, 19), (19, 20)]
21
36
true
22
19
8
8
9,10
16
18
false
16
18
true
16
18
2
erdos
[(0, 1), (1, 15), (1, 16), (1, 22), (2, 3), (2, 4), (3, 5), (4, 6), (6, 9), (6, 13), (7, 8), (7, 9), (8, 9), (8, 13), (9, 13), (10, 11), (12, 18), (12, 19), (12, 20), (14, 15), (15, 22), (16, 22), (17, 19), (18, 19), (19, 20), (19, 21), (20, 21)]
23
27
true
8
0
1
19
12,17,18,20,21
20
10
false
20
10
false
20
10
-1
erdos
[(0, 1), (0, 2), (0, 3), (0, 7), (0, 8), (0, 9), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 9), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 4), (3, 5), (3, 6), (3, 8), (3, 9), (4, 6), (4, 7), (4, 8), (4, 9), (5, 6), (5, 7), (5, 9), (6, 7), (6, 8), (7, 9), (8, 9)]
10
34
true
46
1
7
5
1,2,3,6,7,9
4
2
true
4
2
true
4
2
1
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 6), (0, 8), (0, 9), (1, 2), (1, 3), (1, 4), (1, 5), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 7), (4, 8), (5, 6), (5, 9), (6, 7), (6, 8), (7, 9), (8, 9)]
10
31
true
32
8
7
4
0,1,3,5,7,8
0
3
true
0
3
true
0
3
1
erdos
[(0, 2), (0, 5), (1, 16), (2, 9), (2, 13), (3, 7), (3, 14), (4, 6), (4, 14), (4, 15), (5, 11), (5, 14), (6, 16), (8, 11), (8, 12), (8, 13), (9, 10), (10, 13), (12, 15), (12, 16), (13, 15)]
17
21
true
0
12
3
14
3,4,5
6
14
false
6
14
true
6
14
2
erdos
[(0, 5), (0, 10), (1, 8), (1, 14), (2, 3), (2, 4), (3, 6), (4, 10), (4, 12), (5, 15), (6, 16), (7, 9), (7, 11), (7, 14), (9, 12), (9, 13), (11, 12), (11, 17), (12, 16), (13, 14)]
18
20
true
0
15
1
12
4,9,11,16
13
11
false
13
11
true
13
11
3
erdos
[(0, 1), (1, 2), (1, 3), (2, 3), (3, 5), (3, 7), (4, 5), (4, 6), (4, 7), (5, 6), (5, 7), (6, 7)]
8
12
true
6
4
3
7
3,4,5,6
7
1
false
7
1
true
7
1
2
erdos
[(0, 1), (0, 8), (1, 5), (1, 7), (1, 8), (2, 3), (2, 6), (2, 9), (3, 4), (3, 6), (3, 14), (4, 6), (4, 14), (5, 7), (6, 14), (7, 8), (8, 10), (9, 14), (11, 13), (11, 15), (12, 13), (13, 15)]
16
22
true
9
12
1
9
2,14
11
15
true
11
15
true
11
15
1
erdos
[(0, 1), (0, 10), (0, 11), (0, 15), (1, 15), (1, 16), (1, 19), (1, 20), (2, 6), (2, 10), (2, 11), (2, 14), (2, 15), (3, 5), (3, 7), (3, 20), (4, 7), (4, 14), (5, 10), (5, 15), (5, 18), (5, 19), (6, 8), (6, 9), (6, 10), (6, 15), (6, 16), (6, 19), (7, 12), (9, 10), (9, 12), (9, 14), (9, 15), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (10, 16), (10, 19), (11, 13), (11, 14), (11, 15), (11, 16), (11, 17), (11, 19), (12, 19), (13, 15), (13, 17), (13, 19), (13, 20), (14, 15), (14, 16), (14, 19), (15, 16), (15, 17), (15, 20), (17, 19), (19, 20)]
21
59
true
53
3
3
2
6,10,11,14,15
10
3
false
10
3
true
10
3
2
erdos
[(0, 1), (0, 2), (0, 3), (1, 2), (1, 4), (1, 5), (4, 5), (4, 6), (4, 7), (4, 8), (5, 6), (5, 8), (6, 7), (6, 8), (6, 9), (7, 8), (7, 9), (8, 9)]
10
18
true
12
8
5
1
0,2,4,5
2
3
false
2
3
true
2
3
2
erdos
[(0, 1), (0, 4), (0, 8), (0, 15), (1, 4), (1, 15), (2, 6), (2, 11), (3, 4), (4, 15), (5, 12), (5, 13), (6, 14), (7, 8), (7, 13), (9, 10), (10, 11), (12, 13)]
16
18
true
5
5
2
14
6
7
4
false
7
4
true
7
4
3
erdos
[(0, 1), (0, 3), (0, 4), (1, 2), (5, 25), (6, 10), (7, 8), (8, 13), (9, 10), (9, 11), (9, 12), (13, 14), (14, 15), (14, 16), (15, 16), (17, 18), (19, 20), (20, 21), (21, 22), (22, 23), (23, 24), (24, 25)]
26
22
true
1
7
1
21
20,22
4
24
false
4
24
false
4
24
-1
erdos
[(0, 2), (0, 11), (0, 16), (0, 17), (1, 5), (1, 6), (1, 8), (1, 21), (1, 22), (2, 3), (2, 4), (2, 7), (2, 9), (2, 10), (3, 4), (4, 10), (5, 6), (5, 8), (5, 21), (6, 8), (6, 21), (7, 9), (7, 10), (7, 22), (8, 21), (9, 10), (9, 11), (9, 12), (10, 22), (11, 12), (11, 13), (11, 17), (12, 13), (13, 18), (14, 15), (14, 16), (14, 17), (14, 19), (14, 20), (15, 17), (15, 18), (15, 20), (16, 17), (21, 22)]
23
44
true
25
8
4
20
14,15
7
15
false
7
15
true
7
15
4
erdos
[(0, 3), (0, 4), (1, 7), (1, 8), (1, 10), (2, 9), (2, 16), (3, 4), (3, 7), (4, 8), (4, 9), (5, 6), (5, 7), (5, 15), (6, 7), (6, 10), (6, 13), (7, 8), (8, 14), (8, 15), (9, 14), (10, 13), (11, 12), (11, 15), (12, 14), (12, 15), (14, 15)]
17
27
true
7
8
5
3
0,4,7
5
16
false
5
16
true
5
16
5
erdos
[(0, 1), (0, 5), (0, 6), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 23), (2, 24), (3, 5), (3, 7), (3, 24), (4, 23), (5, 6), (5, 7), (5, 8), (5, 9), (6, 8), (6, 10), (6, 11), (6, 12), (7, 9), (7, 19), (7, 23), (7, 24), (8, 9), (8, 11), (8, 12), (9, 20), (10, 11), (10, 12), (10, 14), (10, 15), (11, 12), (11, 15), (11, 18), (13, 14), (15, 18), (15, 25), (16, 17), (17, 18), (17, 25), (18, 25), (19, 20), (19, 23), (20, 21), (20, 22), (21, 22), (23, 24)]
26
50
true
25
23
5
4
1,2,23
0
23
false
0
23
true
0
23
3
erdos
[(0, 1), (0, 4), (1, 2), (2, 7), (3, 4), (3, 6), (3, 12), (4, 5), (5, 6), (5, 8), (6, 14), (7, 10), (8, 12), (9, 11), (10, 11), (12, 13)]
15
16
true
0
2
2
11
9,10
6
2
false
6
2
true
6
2
5
erdos
[(0, 7), (1, 8), (2, 4), (2, 5), (3, 4), (3, 7), (4, 5), (5, 8), (6, 7)]
9
9
true
1
2
2
2
4,5
4
8
false
4
8
true
4
8
2
erdos
[(0, 5), (0, 7), (0, 8), (0, 13), (0, 16), (0, 17), (0, 18), (0, 21), (0, 22), (0, 28), (1, 3), (1, 7), (1, 10), (1, 15), (1, 17), (1, 21), (1, 26), (2, 3), (2, 12), (2, 13), (2, 14), (2, 17), (2, 21), (2, 28), (3, 7), (3, 11), (3, 12), (3, 13), (3, 14), (3, 16), (3, 19), (3, 23), (3, 24), (3, 25), (3, 26), (3, 28), (4, 6), (4, 7), (4, 9), (4, 10), (4, 12), (4, 13), (4, 17), (4, 20), (4, 22), (4, 23), (4, 24), (4, 26), (4, 28), (5, 7), (5, 8), (5, 9), (5, 13), (5, 16), (5, 17), (5, 20), (5, 22), (5, 24), (5, 25), (5, 27), (6, 7), (6, 8), (6, 10), (6, 11), (6, 13), (6, 14), (6, 15), (6, 23), (6, 25), (6, 27), (7, 9), (7, 14), (7, 16), (7, 18), (7, 20), (7, 24), (7, 26), (8, 10), (8, 11), (8, 12), (8, 16), (8, 17), (8, 19), (8, 20), (8, 21), (8, 23), (8, 24), (8, 28), (9, 14), (9, 16), (9, 19), (9, 20), (9, 23), (9, 24), (9, 26), (10, 13), (10, 17), (10, 18), (10, 20), (10, 22), (10, 23), (10, 25), (10, 27), (11, 12), (11, 13), (11, 14), (11, 16), (11, 17), (11, 18), (11, 25), (11, 26), (12, 13), (12, 14), (12, 15), (12, 16), (12, 22), (12, 23), (12, 24), (12, 27), (12, 28), (13, 14), (13, 16), (13, 18), (13, 22), (13, 24), (13, 27), (14, 19), (14, 24), (14, 26), (14, 27), (15, 16), (15, 17), (15, 20), (15, 22), (15, 23), (15, 24), (15, 27), (16, 17), (16, 19), (16, 20), (16, 21), (16, 22), (16, 27), (17, 19), (17, 22), (17, 23), (17, 26), (18, 20), (18, 21), (18, 22), (18, 27), (19, 21), (19, 23), (19, 27), (20, 21), (20, 25), (20, 27), (20, 28), (21, 25), (21, 27), (21, 28), (22, 25), (22, 26), (22, 27), (23, 25), (23, 28), (24, 27), (24, 28), (25, 26), (25, 28), (26, 27), (26, 28), (27, 28)]
29
173
true
269
17
14
5
0,7,8,9,13,16,17,20,22,24,25,27
6
8
true
6
8
true
6
8
1
erdos
[(0, 1), (0, 2), (0, 3), (0, 5), (0, 6), (1, 2), (1, 4), (1, 7), (1, 8), (2, 4), (2, 5), (2, 8), (3, 5), (3, 6), (4, 7), (4, 8), (4, 21), (5, 6), (6, 9), (7, 8), (7, 20), (7, 21), (8, 20), (9, 14), (9, 15), (10, 11), (10, 12), (11, 12), (13, 14), (13, 15), (14, 15), (16, 17), (16, 18), (16, 19), (16, 20), (17, 18), (17, 19), (17, 20), (18, 19), (19, 20), (20, 21)]
22
41
true
26
9
3
1
0,2,4,7,8
3
21
false
3
21
true
3
21
4
erdos
[(0, 1), (0, 2), (0, 7), (0, 9), (1, 3), (1, 4), (1, 6), (1, 7), (1, 8), (1, 10), (1, 11), (2, 3), (2, 4), (2, 6), (2, 8), (2, 9), (3, 4), (3, 5), (3, 9), (3, 10), (4, 5), (4, 7), (4, 9), (4, 10), (4, 11), (5, 7), (5, 10), (6, 7), (7, 8), (8, 9), (8, 10), (8, 11), (9, 11)]
12
33
true
23
1
8
7
0,1,4,5,6,8
0
8
false
0
8
true
0
8
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (0, 13), (0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (0, 20), (0, 21), (0, 22), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18), (1, 19), (1, 20), (2, 14), (2, 15), (2, 16), (2, 17), (2, 18), (2, 19), (2, 20), (3, 14), (3, 15), (3, 16), (3, 17), (3, 18), (3, 19), (3, 20), (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), (6, 14), (6, 15), (6, 16), (6, 17), (6, 18), (6, 19), (6, 20), (7, 14), (7, 15), (7, 16), (7, 17), (7, 18), (7, 19), (7, 20), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (8, 19), (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), (11, 14), (11, 15), (11, 16), (11, 17), (11, 18), (11, 19), (11, 20), (12, 14), (12, 15), (12, 16), (12, 17), (12, 18), (12, 19), (12, 20), (13, 14), (13, 15), (13, 16), (13, 17), (13, 18), (13, 19), (13, 20), (14, 15), (14, 16), (14, 17), (14, 18), (14, 19), (14, 20), (14, 21), (14, 22), (15, 16), (15, 17), (15, 18), (15, 19), (15, 20), (15, 21), (15, 22), (16, 17), (16, 18), (16, 19), (16, 20), (16, 21), (16, 22), (17, 18), (17, 19), (17, 20), (17, 21), (17, 22), (18, 19), (18, 20), (18, 21), (18, 22), (19, 20), (19, 21), (19, 22), (20, 21), (20, 22)]
23
145
true
455
8
7
11
0,14,15,16,17,18,19,20
13
2
false
13
2
true
13
2
2
erdos
[(0, 3), (0, 5), (0, 6), (1, 7), (1, 8), (2, 4), (2, 9), (3, 5), (3, 7), (3, 8), (4, 9), (5, 7), (5, 8), (5, 9), (6, 9), (7, 8)]
10
16
true
7
8
4
2
4,9
8
0
false
8
0
true
8
0
2
erdos
[(0, 1), (0, 2), (0, 13), (0, 16), (1, 2), (2, 16), (3, 4), (3, 6), (4, 10), (5, 17), (6, 13), (6, 16), (6, 17), (7, 8), (9, 10), (9, 14), (11, 12), (11, 15), (12, 14), (13, 16), (16, 17)]
18
21
true
5
1
2
14
9,12
17
3
false
17
3
true
17
3
2
erdos
[(0, 1), (0, 6), (1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (3, 5), (4, 5), (5, 6)]
7
10
true
4
5
5
2
4,5
6
2
false
6
2
true
6
2
2
erdos
[(0, 4), (1, 4), (2, 3), (2, 4)]
5
4
false
0
2
2
0
4
4
2
true
4
2
true
4
2
1
erdos
[(0, 1), (1, 5), (1, 7), (1, 8), (1, 10), (1, 11), (2, 4), (3, 12), (4, 11), (4, 13), (4, 14), (5, 10), (6, 8), (6, 11), (7, 8), (7, 14), (8, 9), (9, 13), (9, 14), (10, 11), (10, 12), (12, 14)]
15
22
true
3
11
4
1
0,5,7,8,10,11
11
8
false
11
8
true
11
8
2
erdos
[(0, 1), (0, 5), (1, 2), (1, 3), (1, 4), (2, 3), (2, 28), (3, 4), (4, 5), (5, 6), (6, 24), (6, 25), (7, 9), (7, 10), (7, 11), (8, 12), (9, 10), (10, 11), (10, 15), (10, 16), (11, 15), (12, 26), (12, 27), (13, 21), (14, 16), (14, 17), (15, 19), (15, 21), (15, 22), (16, 17), (16, 20), (17, 20), (18, 19), (19, 20), (19, 22), (21, 22), (23, 24), (23, 25), (24, 25), (26, 27), (28, 29)]
30
41
true
12
21
3
3
1,2,4
27
12
true
27
12
true
27
12
1
erdos
[(0, 19), (0, 21), (1, 5), (1, 9), (2, 21), (3, 8), (3, 12), (3, 17), (4, 20), (6, 24), (7, 14), (8, 11), (8, 13), (8, 17), (9, 23), (10, 18), (10, 22), (12, 15), (14, 16), (14, 25), (16, 21), (16, 25), (20, 21), (21, 24), (22, 24)]
26
25
true
2
13
1
20
4,21
14
4
false
14
4
true
14
4
4
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 4), (1, 6), (1, 8), (1, 9), (2, 3), (2, 4), (3, 4), (5, 6), (5, 7), (5, 9), (6, 7), (6, 9), (7, 9), (8, 9)]
10
18
true
11
5
3
4
0,1,2,3
5
8
false
5
8
true
5
8
2
erdos
[(0, 21), (0, 26), (1, 13), (1, 18), (1, 20), (1, 26), (1, 29), (1, 33), (2, 17), (2, 26), (2, 33), (3, 6), (3, 8), (3, 12), (3, 16), (3, 26), (3, 27), (3, 33), (4, 7), (4, 23), (5, 23), (6, 8), (6, 18), (7, 21), (8, 16), (9, 19), (9, 27), (10, 21), (11, 31), (12, 14), (12, 22), (12, 29), (12, 30), (13, 32), (14, 25), (15, 25), (15, 30), (16, 20), (17, 24), (18, 33), (20, 26), (21, 29), (21, 30), (21, 32), (24, 31), (25, 30), (26, 32), (28, 29)]
34
48
true
5
27
2
8
3,6,16
1
31
false
1
31
true
1
31
5
erdos
[(0, 1), (0, 2), (0, 4), (0, 6), (0, 10), (0, 11), (0, 12), (0, 14), (0, 16), (0, 17), (1, 6), (1, 8), (1, 10), (1, 11), (1, 18), (2, 4), (2, 5), (2, 11), (2, 18), (2, 19), (3, 4), (3, 9), (4, 10), (4, 11), (4, 12), (5, 6), (5, 11), (5, 13), (5, 14), (5, 15), (5, 16), (6, 9), (6, 17), (6, 19), (7, 19), (9, 11), (10, 11), (10, 16), (10, 17), (10, 18), (10, 19), (11, 18), (11, 19), (12, 19), (15, 19), (16, 18)]
20
46
true
23
8
1
2
0,4,5,11,18,19
2
1
false
2
1
true
2
1
2
erdos
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
5
10
true
10
0
4
4
0,1,2,3
1
0
true
1
0
true
1
0
1
erdos
[(0, 4), (0, 5), (1, 2), (1, 4), (2, 3)]
6
5
false
0
1
2
0
4,5
2
5
false
2
5
true
2
5
4
erdos
[(0, 1), (0, 4), (0, 5), (0, 11), (0, 12), (0, 13), (0, 14), (1, 4), (1, 5), (1, 11), (1, 12), (1, 13), (1, 14), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5), (4, 12), (6, 7), (6, 8), (6, 19), (7, 8), (8, 19), (9, 10), (9, 16), (9, 17), (9, 18), (10, 15), (10, 16), (10, 17), (10, 18), (11, 12), (11, 13), (11, 14), (12, 13), (12, 14), (13, 14), (15, 16), (15, 17), (15, 18), (16, 17), (16, 18), (17, 18)]
20
45
true
48
6
3
11
0,1,12,13,14
15
5
false
15
5
false
15
5
-1
erdos
[(0, 3), (0, 4), (0, 5), (0, 6), (1, 5), (1, 6), (2, 3), (2, 4), (2, 7), (2, 8), (2, 9), (3, 4), (4, 6), (5, 6), (5, 17), (7, 8), (7, 12), (7, 15), (8, 9), (8, 12), (8, 15), (9, 12), (10, 12), (10, 18), (10, 19), (11, 14), (12, 15), (13, 14), (13, 15), (16, 19), (18, 19)]
20
31
true
13
18
2
1
5,6
9
7
false
9
7
true
9
7
2
erdos
[(0, 2), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
5
7
true
4
1
3
4
1,2,3
0
3
false
0
3
true
0
3
2