Triangle-free equimatchable graphs

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Büyükçolak Y., Özkan S., Gözüpek D.

Journal of Graph Theory, cilt.99, sa.3, ss.461-484, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 99 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1002/jgt.22750
  • Dergi Adı: Journal of Graph Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.461-484
  • Anahtar Kelimeler: equimatchable, factor-critical, girth, graph families, triangle-free, RECOGNITION
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

© 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.