Coloring and the Lovasz Local Lemma

被引：3

作者：

Chen, Xing ^{[1
]}

Du, Zhihua ^{[2
]}

Meng, Jixiang ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China

[2] Xinjiang Normal Univ, Dept Math & Informat Sci, Urumqi 830054, Xinjiang, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2010年 / 23卷 / 03期

关键词：

Lovasz Local Lemma; Lopsidependency graph; t-coloring;

D O I：

10.1016/j.aml.2009.02.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Lovasz Local Lemma yields sufficient conditions for a hypergraph to be 2-colorable, that is, to have a coloring of the points blue or red such that no edge is monochromatic. The method yields a general theorem, which shows for example, if H is a hypergraph in which each edge contains at least 9 points and each point is contained in at most 11 edges, then H is 2-colorable. In this paper, we use the 'lopsided' version of the Local Lemma to give some sufficient conditions on t-coloring to hypergraphs and 2-coloring to hypergraphs such that each edge contains at least 2 points of each color. (C) 2009 Published by Elsevier Ltd

引用

页码：219 / 221

页数：3

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