The Number of Independent Sets in Graphs

被引：9
|
作者：
Sapozhenko, A. A. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119991, Russia
来源：
MOSCOW UNIVERSITY MATHEMATICS BULLETIN | 2007年 / 62卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
D O I：
10.3103/S0027132207030072
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The following theorem is proved: Let G be a k-regular graph with n vertices such that the maximal size of an independent set of the graph G is equal to mu. Then i(G) <= 2(mu log) (1+ n/2 mu) + O( n root k(-1) log k). This statement is generalized to the case of quasi- regular graphs. As a corollary, an upper bound for the number of independent sets in extenders is obtained.
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页码：116 / 118
页数：3
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