A pair of forbidden subgraphs and perfect matchings in graphs of high connectivity

Jun Fujisawa, Shinya Fujita, Michael D. Plummer, Akira Saito, Ingo Schiermeyer

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Sumner [7] proved that every connected K 1,3-free graph of even order has a perfect matching. He also considered graphs of higher connectivity and proved that if m ≥ 2, every m-connected K 1,m+1-free graph of even order has a perfect matching. In [6], two of the present authors obtained a converse of sorts to Sumner's result by asking what single graph one can forbid to force the existence of a perfect matching in an m-connected graph of even order and proved that a star is the only possibility. In [2], Fujita et al. extended this work by considering pairs of forbidden subgraphs which force the existence of a perfect matching in a connected graph of even order. But they did not settle the same problem for graphs of higher connectivity. In this paper, we give an answer to this problem. Together with the result in [2], a complete characterization of the pairs is given.

Original languageEnglish
Pages (from-to)703-723
Number of pages21
JournalCombinatorica
Volume31
Issue number6
DOIs
Publication statusPublished - 2011 Dec 1

    Fingerprint

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

Cite this