Enumerating maximal independent sets with applications to graph colouring

被引：83

作者：

Byskov, JM

机构：

[1] Univ Aarhus, Dept Comp Sci, BRICS, DK-8200 Aarhus N, Denmark

[2] Univ Calif Irvine, Irvine, CA 92717 USA

来源：

OPERATIONS RESEARCH LETTERS | 2004年 / 32卷 / 06期

关键词：

maximal independent set; graph colouring; chromatic number; graph algorithms; extremal graphs;

D O I：

10.1016/j.orl.2004.03.002

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We give tight upper bounds on the number of maximal independent sets of size k (and at least k and at most k) in graphs with n vertices. As an application of the proof, we construct improved algorithms for graph colouring and computing the chromatic number of a graph. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：547 / 556

页数：10

共 14 条

[1]

[Anonymous], 1999, HDB COMBINATORIAL OP

[2]

Byskov JM, 2003, SIAM PROC S, P456

[3]

BYSKOV JM, 2002, RES SERIES BRICS

[4] ALGORITHM FOR CHROMATIC NUMBER OF A GRAPH [J].

CHRISTOFIDES, N .

COMPUTER JOURNAL, 1971, 14 (01) :38-+

[5]

Croitoru C., 1979, P 3 C OP RES BAB BOL, P55

[6]

Eppstein D., 2003, Journal of Graph Algorithms and Applications, V7, DOI 10.7155/jgaa.00064

[7]

Eppstein D, 2001, SIAM PROC S, P329

[8] THE NUMBER OF MAXIMAL INDEPENDENT SETS IN TRIANGLE-FREE GRAPHS [J].

HUJTER, M ;

TUZA, Z .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 1993, 6 (02) :284-288

[9]

Lawler E., 1976, INFORM PROCESS LETT, V5, P66

[10]

MADSEN BA, 2002, RES SERIES BRICS

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