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searching for Monochromatic triangle 6 found (11 total)

Sim (game) (492 words) [view diff] exact match in snippet view article

two-coloring of the complete graph on 6 vertices (K6) must contain a monochromatic triangle, and therefore is not a tied position. This will also apply to any

Theorem on friends and strangers (622 words) [view diff] exact match in snippet view article find links to article

words, whatever colours you use, there will always be at least one monochromatic triangle ( that is, a triangle all of whose edges have the same color ).

Almost surely (1,425 words) [view diff] case mismatch in snippet view article find links to article

Prasad (January 2006). "A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring". Memoirs of the American Mathematical Society

Andrew M. Gleason (5,383 words) [view diff] exact match in snippet view article find links to article

edges colored with three colors, then it necessarily contains a monochromatic triangle. As they showed, R(3,3,3) = 17; this remains the only nontrivial

Ramsey's theorem (7,887 words) [view diff] exact match in snippet view article find links to article

there are at most 6 × 6 = 36 such triples. Secondly, for any non-monochromatic triangle (xyz), there exist precisely two such triples. Therefore, there

Edge coloring (8,472 words) [view diff] exact match in snippet view article find links to article

the edges of the graph K6 are 2-colored, there will always be a monochromatic triangle. A path in an edge-colored graph is said to be a rainbow path if