Colorful subgraphs in Kneser-like graphs |
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Authors: | Gbor Simonyi Gbor Tardos |
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Institution: | aAlfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1364 Budapest, POB 127, Hungary;bSchool of Computing Science, Simon Fraser University, Burnaby BC, Canada V5A 1S6 |
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Abstract: | Combining Ky Fan’s theorem with ideas of Greene and Matoušek we prove a generalization of Dol’nikov’s theorem. Using another variant of the Borsuk–Ulam theorem due to Tucker and Bacon, we also prove the presence of all possible completely multicolored t-vertex complete bipartite graphs in t-colored t-chromatic Kneser graphs and in several of their relatives. In particular, this implies a generalization of a recent result of G. Spencer and F.E. Su. |
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