Perfect matchings avoiding prescribed edges in a star-free graph

Yoshimi Egawa, Jun Fujisawa, Michael D. Plummer, Akira Saito, Tomoki Yamashita

Research output: Contribution to journalArticle

Abstract

Aldred and Plummer (1999) have proved that every m-connected K1<inf>,m-k+2</inf>-free graph of even order contains a perfect matching which avoids k prescribed edges. They have also proved that the result is best possible in the range 1≤k≤12(m+1). In this paper, we show that if 12(m+2)≤k≤m-1, their result is not best possible. We prove that if m≥4 and 12(m+2)≤k≤m-1, every K1<inf>,⌈2m-k+43⌉</inf>-free graph of even order contains a perfect matching which avoids k prescribed edges. While this is a best possible result in terms of the order of a forbidden star, if 2m-k+4≡0(mod3), we also prove that only finitely many sharpness examples exist.

Original languageEnglish
Pages (from-to)2260-2274
Number of pages15
JournalDiscrete Mathematics
Volume338
Issue number12
DOIs
Publication statusPublished - 2015 Jun 22

Keywords

  • Extendability
  • Forbidden subgraph
  • Perfect matching
  • Star-free graphs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

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