An improved lower bound on the independence number of a graph

被引：4

作者：

Henning, Michael A. ^{[1
]}

Loewenstein, Christian ^{[2
]}

机构：

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

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

来源：

DISCRETE APPLIED MATHEMATICS | 2014年 / 179卷

基金：

新加坡国家研究基金会;

关键词：

Independence; Vertex-cover; MAXIMUM DEGREE; TERMS; SIZE; DOMINATION; ORDER;

D O I：

10.1016/j.dam.2014.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The independence number of a graph G, denoted alpha(G), is the maximum cardinality of an independent set of vertices in G. Our main result is the strengthening of a lower bound for the independence number of a graph due to Lowenstein'et al. (2011) who proved that if G is a connected graph of order n and size m, then alpha(G) >= 2/3 n- 1/4m - 1/3. We show that if G does not belong to a specific family of graphs, then alpha(G) > in 2/3n - 1/4m. Further, we characterize the graphs G for which alpha(G) <= 2/3n - 1/4 m. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：120 / 128

页数：9

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