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File:Ramsey theorem visual proof.svg

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Description Proof without words of the two-colour case of Ramsey's theorem by CMG Lee.
Due to the pigeonhole principle, there are at least 3 edges of the same colour (dashed purple) from an arbitrary vertex v. Calling 3 of the vertices terminating these edges r, s and t, if the edge rs, st or tr (solid black) had this colour, it would complete the triangle with v. But if not, each must be oppositely coloured, completing triangle rst of that colour.
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Author Cmglee

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Date/TimeThumbnailDimensionsUserComment
current17:33, 7 January 2024Thumbnail for version as of 17:33, 7 January 2024512 × 512 (521 bytes)Cmglee (talk | contribs)Align text and remove construction shapes
17:28, 7 January 2024Thumbnail for version as of 17:28, 7 January 2024512 × 512 (1 KB)Cmglee (talk | contribs){{Information |Description=Proof without words of Ramsey's theorem by CMG Lee. Due to the pigeonhole principle, there are at least 3 edges from an arbitrary vertex ''v'' of the same colour (dashed purple). Calling 3 of the vertices terminating these edges ''r'', ''s'' and ''t'', if the edge ''rs'', ''st'' or ''tr'' (solid black) has this colour, it would complete the triangle with ''v''. But if not, each must be oppositely coloured, completing a triangle of that colour. |Source={{own}} |Date...

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