Choosability with separation of complete multipartite graphs and hypergraphs
Combinatorics
2011-09-15 v1
Abstract
For a hypergraph G and a positive integer s, let \chi_{\ell} (G,s) be the minimum value of l such that G is L-colorable from every list L with |L(v)|=l for each v\in V(G) and |L(u)\cap L(v)|\leq s for all u, v\in e\in E(G). This parameter was studied by Kratochv\'{i}l, Tuza and Voigt for various kinds of graphs. Using randomized constructions we find the asymptotics of \chi_{\ell} (G,s) for balanced complete multipartite graphs and for complete k-partite k-uniform hypergraphs.
Cite
@article{arxiv.1109.2969,
title = {Choosability with separation of complete multipartite graphs and hypergraphs},
author = {Zoltán Füredi and Alexandr Kostochka and Mohit Kumbhat},
journal= {arXiv preprint arXiv:1109.2969},
year = {2011}
}
Comments
9 pages