Colorful Subhypergraphs in Uniform Hypergraphs
Meysam Alishahi

TL;DR
This paper generalizes topological methods to establish new bounds on the chromatic and local chromatic numbers of uniform hypergraphs, extending previous results on colorful subhypergraphs in Kneser hypergraphs.
Contribution
It introduces new generalizations of the $ ext{Z}_p$-Tucker lemma, improving upon Meunier's results and providing novel lower bounds for hypergraph chromatic numbers.
Findings
New lower bounds for chromatic numbers of uniform hypergraphs
Enhanced results on colorful subhypergraphs in Kneser hypergraphs
Generalizations of the $ ext{Z}_p$-Tucker lemma
Abstract
There are several topological results ensuring the existence of a large complete bipartite subgraph in any properly colored graph satisfying some special topological regularity conditions. In view of -Tucker lemma, Alishahi and Hajiabolhassan [{\it On the chromatic number of general Kneser hypergraphs, Journal of Combinatorial Theory, Series B, 2015}] introduced a lower bound for the chromatic number of Kneser hypergraphs . Next, Meunier [{\it Colorful subhypergraphs in Kneser hypergraphs, The Electronic Journal of Combinatorics, 2014}] improved their result by proving that any properly colored general Kneser hypergraph contains a large colorful -partite subhypergraph provided that is prime. In this paper, we give some new generalizations of -Tucker lemma. Hence, improving Meunier's result in some…
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