SIMPLE Σ_r-HOMOTOPY TYPES OF HOM COMPLEXES AND BOX COMPLEXES ASSIGNED TO r-GRAPHS

Abstract

For a pair of graphs, Lovász introduced a polytopal complex called the Hom complex in order to estimate topological lower bounds for chromatic numbers of graphs. The definition is generalized to hypergraphs. Given an r-graph H, we compare the Hom complex of the complete r-partite r-graph and H with the box complex of H invented by Alon, Frankl and Lovász. We verify that both complexes which are equipped with right actions of the symmetric group on r letters ∑_r, are of the same simple ∑_r -homotopy type

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Kyushu University Institutional Repository

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oai:catalog.lib.kyushu-u.ac.jp:2324/1397753Last time updated on 5/27/2016

This paper was published in Kyushu University Institutional Repository.

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