Chinese Quarterly Journal of Mathematics ›› 2022, Vol. 37 ›› Issue (4): 430-431.doi: 10.13371/j.cnki.chin.q.j.m.2022.04.011

Previous Articles     Next Articles

A Note on the Girth of 3-Regular Hamiltonian Graph

  

  1. 1. Department of Mathematics, Nanjing University, Nanjing 210093, China; 2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
  • Received:2022-11-14 Online:2022-12-30 Published:2022-12-30
  • Contact: YUAN Jin-jiang (1965-), male, native of Hejin, Shanxi, professor of Zhengzhou University, engages in scheduling theory. E-mail:yuanjj@zzu.edu.cn
  • About author:: 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.
  • 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). 

PDF (PC)

69

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 

CLC Number: 

Copyright © Chinese Quarterly Journal of Mathematics, All Rights Reserved.
Tel: 0371-23881698　E-mail: sxjk@henu.edu.cn　QQ: 2454327236
Powered by Beijing Magtech Co., Ltd.