Chinese Quarterly Journal of Mathematics ›› 2022, Vol. 37 ›› Issue (4): 432-440.doi: 10.13371/j.cnki.chin.q.j.m.2022.04.012

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Characterizations of Cycle-Forced 2-Connected Claw-Free Cubic Graphs

  

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
  • Received:2022-11-14 Online:2022-12-30 Published:2022-12-30
  • Contact: ZHANG Yi-ran (1996-), female, native of Zhengzhou, Henan, student of Zhengzhou University, engages in graph theory; E-mail:zhangyiran1125@163.com
  • About author:ZHANG Yi-ran (1996-), female, native of Zhengzhou, Henan, student of Zhengzhou University, engages in graph theory; WANG Xiu-mei (1972-), female, native of Zhengzhou, Henan, professor of Zhengzhou University, Ph.D supervisor, Ph.D, engages in graph theory.
  • Supported by:
    Supported by National Natural Science Foundation of China (Grant Nos. 12171440 and 11971445). 

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Abstract: Let G be a graph and C be an arbitrary even cycle of G. The graph G is called a cycle-forced graph if G−V (C) has a unique perfect matching. When C is an arbitrary induced even cycle of G, G is called an induced-cycle-forced graph. If G−V (C) has no perfect matching, G is said to be cycle-bad. This paper gives characterizations of these three type of graphs in the class of 2-connected claw-free cubic graphs. 

Key words: Perfect matching, Cubic graph, Claw-free graph, Cycle-forced graph

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