### 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*.Original language | English |
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Pages (from-to) | 287-298 |

Journal | Journal of Combinatorial Theory, Series B, Graph theory |

Volume | 99 |

Issue number | 2 |

Publication status | Published - 2009 |

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## Cite this

Cioaba, S. M., Gregory, D. A., & Haemers, W. H. (2009). Matchings in regular graphs from eigenvalues.

*Journal of Combinatorial Theory, Series B, Graph theory*,*99*(2), 287-298.