A pair of forbidden subgraphs and perfect matchings

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

Research output: Contribution to journalArticle

25 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)315-324
Number of pages10
JournalJournal of Combinatorial Theory. Series B
Issue number3
Publication statusPublished - 2006 May 1


  • Forbidden subgraph
  • Near-perfect matching
  • Perfect matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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    Fujita, S., Kawarabayashi, K. I., Leonardo Lucchesi, C., Ota, K., Plummer, M. D., & Saito, A. (2006). A pair of forbidden subgraphs and perfect matchings. Journal of Combinatorial Theory. Series B, 96(3), 315-324. https://doi.org/10.1016/j.jctb.2005.08.002