Triangle-free equimatchable graphs

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Büyükçolak Y., Özkan S., Gözüpek D.

Journal of Graph Theory, vol.99, no.3, pp.461-484, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 99 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1002/jgt.22750
  • Journal Name: Journal of Graph Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, MathSciNet, zbMATH
  • Page Numbers: pp.461-484
  • Keywords: equimatchable, factor-critical, girth, graph families, triangle-free, RECOGNITION
  • Kocaeli University Affiliated: No

Abstract

© 2021 Wiley Periodicals LLCA graph is called equimatchable if all of its maximal matchings have the same size. Frendrup et al. provided a characterization of equimatchable graphs with girth at least 5. In this paper, we extend this result by providing a complete structural characterization of equimatchable graphs with girth at least 4, that is, equimatchable graphs with no triangle, by identifying the equimatchable triangle-free graph families. Our characterization also extends the result given by Akbari et al., which proves that the only connected triangle-free equimatchable (Formula presented.) -regular graphs are (Formula presented.), (Formula presented.), and (Formula presented.), where (Formula presented.) is a positive integer. Given a nonbipartite graph, our characterization implies a linear time recognition algorithm for triangle-free equimatchable graphs.