Characterizations of Cycle-Forced 2-Connected Claw-Free&nbsp;Cubic Graphs

ZHANG Yi-ran, WANG Xiu-mei

doi:10.13371/j.cnki.chin.q.j.m.2022.04.012

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 4: 432 - 440

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.04.012

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

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School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

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.

Received date: 2022-11-14

Online published: 2022-12-30

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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ZHANG Yi-ran, WANG Xiu-mei . Characterizations of Cycle-Forced 2-Connected Claw-Free Cubic Graphs[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(4) : 432 -440 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.012

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