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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