Colorful Subhypergraphs in Kneser Hypergraphs

Frédéric Meunier

Abstract


Using a $\mathbb{Z}_q$-generalization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number of Kneser hypergraphs (using a natural definition of what can be the local chromatic number of a uniform hypergraph).

Keywords


colorful complete $p$-partite hypergraph; combinatorial topology; Kneser hypergraphs; local chromatic number

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