A new lower bound on the independence number of a graph and applications

被引：0

作者：

Henning, Michael A. ^{[1
]}

Loewenstein, Christian ^{[2
]}

Southey, Justin ^{[1
]}

Yeo, Anders ^{[1
,3
]}

机构：

[1] Univ Johannesburg, Dept Math, Auckland Pk, ZA-2006 Johannesburg, South Africa

[2] Univ Ulm, Inst Optimizat & Operat Res, D-89081 Ulm, Germany

[3] Singapore Univ Technol & Design, Singapore 138682, Singapore

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2014年 / 21卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

independence; clique; transversal; SMALL TRANSVERSALS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The independence number of a graph C, denoted a(G), is the maximum cardinality of an independent set of vertices in G. The independence number is one of the most fundamental and well-studied graph parameters. In this paper, we strengthen a result of Fajtlowicz [Combinatorica 4 (1984), 35-38] on the independence of a graph given its maximum degree and maximum clique size. As a consequence of our result we give bounds on the independence number and transversal number of 6-uniform hypergraphs with maximum degree three. This gives support for a conjecture due to Tuza and Vestergaard [Discussiones Math. Graph Theory 22 (2002), 199-210] that if H is a 3-regular 6-uniform hypergraph of order n, then T (H) <= n/4.

引用

页数：12

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