Geodesic
Colorful subhypergraphs in uniform hypergraphs
Meysam Alishahi1
1School of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
The electronic journal of combinatorics, Tome 24 (2017) no. 1
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There are several topological results ensuring in any properly colored graph the existence of a colorful complete bipartite subgraph, whose order is bounded from below by some topological invariants of some topological spaces associated to the graph. Meunier [Colorful subhypergraphs in Kneser hypergraphs, The Electronic Journal of Combinatorics, 2014] presented the first colorful type result for uniform hypergraphs. In this paper, we give some new generalizations of the $\mathbb{Z}_p$-Tucker lemma and by use of them, we improve Meunier's result and some other colorful results by Simonyi, Tardif, and Zsbán [Colourful theorems and indices of homomorphism complexes, The Electronic Journal of Combinatorics, 2014] and by Simonyi and Tardos [Colorful subgraphs in Kneser-like graphs, European Journal of Combinatorics, 2007] to uniform hypergraphs. Also, we introduce some new lower bounds for the chromatic number and local chromatic number of uniform hypergraphs. A hierarchy between these lower bounds is presented as well.
DOI : 10.37236/6154
Classification : 05C15, 05C65
Mots-clés : chromatic number of hypergraphs, \(\mathbb{Z}_p\)-Tucker-Ky Fan lemma, colorful complete hypergraph, \(\mathbb{Z}_p\)-box-complex, \(\mathbb{Z}_p\)-Hom-complex

Meysam Alishahi  1

1 School of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran 
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Meysam Alishahi. Colorful subhypergraphs in uniform hypergraphs. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6154

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