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Equimatchable regular graphs

Akbari, S ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1002/jgt.22138
  3. Publisher: Wiley-Liss Inc , 2018
  4. Abstract:
  5. A graph is called equimatchable if all of its maximal matchings have the same size. Kawarabayashi, Plummer, and Saito showed that the only connected equimatchable 3-regular graphs are K4 and K3, 3. We extend this result by showing that for an odd positive integer r, if G is a connected equimatchable r-regular graph, then G ϵ {Kr+1, Kr,r}. Also it is proved that for an even r, a connected triangle-free equimatchable r-regular graph is isomorphic to one of the graphs C5, C7, and Kr,r. © 2017 Wiley Periodicals, Inc
  6. Keywords:
  7. 05C75 ; 2010 AMS Subject Classification Number: 05C70 ; Equimatchable ; Regular graph ; Triangle-free graph ; Geometry ; 05C75 ; Equimatchable ; Regular graphs ; Subject classification ; Triangle-free graphs ; Graph theory
  8. Source: Journal of Graph Theory ; Volume 87, Issue 1 , 2018 , Pages 35-45 ; 03649024 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.22138