A pair of forbidden subgraphs and perfect matchings

  • Authors:

  • Shinya Fujita;Ken-ichi Kawarabayashi;Claudio Leonardo Lucchesi;Katsuhiro Ota;Michael D. Plummer;Akira Saito

  • Affiliations:

  • Department of Mathematics, Keio University, Kohoku-Ku, Yokohama, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Miyagi, Japan;Institute of Computing, UNICAMP, Campinas, Brazil;Department of Mathematics, Keio University, Kohoku-Ku, Yokohama, Japan;Department of Mathematics, Vanderbilt University, Nashville, TN;Department of Computer Science, Nihon University, Setagaya-Ku, Tokyo, Japan

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2006

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Abstract

In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to be H-free if no graph in H is an induced subgraph of G. We completely characterize the set H such that every connected H-free graph of sufficiently large even order has a perfect matching in the following cases.(1) Every graph in H is triangle-free. (2) H consists of two graphs (i.e. a pair of forbidden subgraphs).A matching M in a graph of odd order is said to be a near-perfect matching if every vertex of G but one is incident with an edge of M. We also characterize H such that every H-free graph of sufficiently large odd order has a near-perfect matching in the above cases.