A Note on the Girth of 3-Regular Hamiltonian Graph

ZHAO Qiu-lan, YUAN Jin-jiang

doi:10.13371/j.cnki.chin.q.j.m.2022.04.011

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 4: 430 - 431

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.04.011

A Note on the Girth of 3-Regular Hamiltonian Graph

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1. Department of Mathematics, Nanjing University, Nanjing 210093, China; 2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

: ZHAO Qiu-lan (1986-), female, native of Zhoukou, Henan, associate professor of Nanjing University, engages in combinatorial optimization; YUAN Jin-jiang (1965-), male, native of Hejin, Shanxi, professor of Zhengzhou University, engages in scheduling theory.

Received date: 2022-11-14

Online published: 2022-12-30

Supported by

Supported by National Natural Science Foundation of China (Grant No. 12071442) and the Fundamental Research Funds for the Central Universities under (Grant No. 020314380035).

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Abstract

It is well-known that the Petersen graph is nonhamiltonian. A very short proof for this result was presented in [2] due to D. B. West. In this note, by extending the proof technique in [2], we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most (n+ 4)/3.

Key words： Girth; Hamiltonian graph; 3-Regular graph

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ZHAO Qiu-lan, YUAN Jin-jiang . A Note on the Girth of 3-Regular Hamiltonian Graph[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(4) : 430 -431 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.011

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