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.
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页码：120 / 128
页数：9
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