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import json
from itertools import combinations
def verify_ramsey_coloring():
"""Verify R(5,5,5) coloring with n=52 and 3 colors."""
# Load the cleaned verification data
with open('ramsey_verification.json') as f:
data = json.load(f)
n, k, colors = data['n'], data['k'], data['num_colors']
assignment = data['assignment']
# Reconstruct edge coloring from assignment
edges = [(i, j) for i in range(n) for j in range(i + 1, n)]
coloring = {}
for idx, (u, v) in enumerate(edges):
for c in range(colors):
if assignment[idx * colors + c] > 0.5:
coloring[(u, v)] = c
break
# Verify all K5 cliques are not monochromatic
total_cliques = 0
monochromatic_cliques = 0
for clique in combinations(range(n), k):
clique_edges = [coloring[(u, v)] for u, v in combinations(clique, 2)]
total_cliques += 1
if len(set(clique_edges)) == 1: # All edges same color
monochromatic_cliques += 1
print(f"R({k},{k},{k}) verification results:")
print(f"Total K{k} cliques: {total_cliques:,}")
print(f"Monochromatic K{k} cliques: {monochromatic_cliques}")
print(f"Valid coloring: {'Yes' if monochromatic_cliques == 0 else 'No'}")
return monochromatic_cliques == 0
if __name__ == "__main__":
verify_ramsey_coloring() |