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.
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页数：12
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