Journal of East China Normal University(Natural Science) >

2020 , Vol. 2020 >Issue 4: 45 - 50

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911013

Mathematics

A new cycle structure theorem for Hamiltonian graphs

  • LI Jingyun ,
  • REN Han
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  • 1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China;
    2. Shanghai Huimin Middle School, Shanghai 200065, China

Received date: 2019-03-12

  Online published: 2020-07-20

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Abstract

An $ n $-vertex graph is called pancyclic if it contains a cycle of length $ k $ for every $ k\;(3\leqslant k\leqslant n) $. Pancyclic graphs are an important topic in cycle theory. In this paper, we demonstrate pancyclicity by showing that the distance between two non-adjacent vertices on a Hamiltonian cycle is 3.

Key words： Hamiltonian graph; pancyclic graph; cycle

Cite this article

LI Jingyun , REN Han . A new cycle structure theorem for Hamiltonian graphs[J]. Journal of East China Normal University(Natural Science), 2020 , 2020(4) : 45 -50 . DOI: 10.3969/j.issn.1000-5641.201911013

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