A Ramsey‐type result for the hypercube |
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Authors: | Noga Alon Rado Radoi
i Benny Sudakov Jan Vondrk |
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Institution: | Noga Alon,Rado? Radoi?i?,Benny Sudakov,Jan Vondrák |
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Abstract: | We prove that for every fixed k and ? ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2 ?. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k‐edge coloring of a sufficiently large Qn contains a monochromatic copy of H. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 196–208, 2006 |
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Keywords: | Ramsey theory hypercube monochromatic cycles |
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