Matchings in regular graphs from eigenvalues

Authors:
Sebastian M. Cioabă;David A. Gregory;Willem H. Haemers
Affiliations:
Department of Computer Science, University of Toronto, Ontario, M5S 3G4, Canada;Department of Mathematics, Queen's University at Kingston, Ontario, K7L 3N6, Canada;Department of Economics and Operations Research, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands
Venue:
Journal of Combinatorial Theory Series B
Year:
2009

Citing 4
Cited 2

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Matrix analysis
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Journal of Combinatorial Theory Series B
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Global Connectivity And Expansion: Long Cycles and Factors In f-Connected Graphs

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Edge-Connectivity, Eigenvalues, and Matchings in Regular Graphs

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Regular Graphs, Eigenvalues and Regular Factors

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Abstract

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.