Journal of East China Normal University(Natural Science) ›› 2020, Vol. 2020 ›› Issue (4): 45-50.doi: 10.3969/j.issn.1000-5641.201911013

• Mathematics • Previous Articles     Next Articles

A new cycle structure theorem for Hamiltonian graphs

LI Jingyun1,2, REN Han1   

  1. 1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China;
    2. Shanghai Huimin Middle School, Shanghai 200065, China
  • Received:2019-03-12 Published:2020-07-20

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

CLC Number: