Matchings in regular graphs from eigenvalues

被引：66

作者：

Cioaba, Sebastian M. ^{[1
]}

Gregory, David A. ^{[2
]}

Haemers, Willem H. ^{[3
]}

机构：

[1] Univ Toronto, Dept Comp Sci, Toronto, ON M5S 3G4, Canada

[2] Queens Univ, Dept Math, Kingston, ON K7L 3N6, Canada

[3] Tilburg Univ, Dept Econ & Operat Res, NL-5000 LE Tilburg, Netherlands

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2009年 / 99卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Matchings; Eigenvalues; Spectral radius;

D O I：

10.1016/j.jctb.2008.06.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a connected k-regular graph of order n. We find a best upper bound (in terms of k) on the third largest eigenvalue that is sufficient to guarantee that G has a perfect matching when n is even, and a matching of order n - 1 when n is odd. We also examine how other eigenvalues affect the size of matchings in G. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：287 / 297

页数：11

共 50 条

[1] EDGE-CONNECTIVITY, EIGENVALUES, AND MATCHINGS IN REGULAR GRAPHS
Suil, O.
Cioaba, Sebastian M.
[J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2010, 24 (04) : 1470 - 1481
[2] MATCHINGS IN REGULAR GRAPHS
NADDEF, D
PULLEYBLANK, WR
[J]. DISCRETE MATHEMATICS, 1981, 34 (03) : 283 - 291
[3] Regular factors of regular graphs from eigenvalues
Lu, Hongliang
[J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2010, 17 (01):
[4] Random Matchings in Regular Graphs
Jeff Kahn
Jeong Han Kim
[J]. Combinatorica, 1998, 18 : 201 - 226
[5] On maximum matchings and eigenvalues of benzenoid graphs
Fajtlowicz, S
John, PE
Sachs, H
[J]. CROATICA CHEMICA ACTA, 2005, 78 (02) : 195 - 201
[6] Maximum matchings in regular graphs
Ye, Dong
[J]. DISCRETE MATHEMATICS, 2018, 341 (05) : 1195 - 1198
[7] Random matchings in regular graphs
Kahn, J
Kim, JH
[J]. COMBINATORICA, 1998, 18 (02) : 201 - 226
[8] Fractional matchings on regular graphs
Guan, Xiaxia
Ma, Tianlong
[J]. JOURNAL OF SUPERCOMPUTING, 2024, 80 (13): : 18942 - 18953
[9] Regular Graphs, Eigenvalues and Regular Factors
Lu, Hongliang
[J]. JOURNAL OF GRAPH THEORY, 2012, 69 (04) : 349 - 355
[10] Regular factors and eigenvalues of regular graphs
Gu, Xiaofeng
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2014, 42 : 15 - 25

← 1 2 3 4 5 →