Matchings in regular graphs from eigenvalues
Cioaba,S.M. Gregory,D.A. Haemers,W.H.
Cioaba,S.M.
Gregory,D.A.
Haemers,W.H.
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 n - 1 order when n is odd. We also examine how other eigenvalues affect the size of matchings in G.
Description
Date
2009
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Research Projects
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Citation
Cioaba, S M, Gregory, D A & Haemers, W H 2009, 'Matchings in regular graphs from eigenvalues', Journal of Combinatorial Theory Series B, vol. 99, no. 2, pp. 287-298.