数学

关于Hamilton图的新的圈结构定理

  • 李静云 ,
  • 任韩
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  • 1. 华东师范大学 数学科学学院, 上海 200241;
    2. 上海市回民中学,上海 200065

收稿日期: 2019-03-12

  网络出版日期: 2020-07-20

基金资助

国家自然科学基金(11171114)

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

摘要

设$ G $是一个$ n $阶图, 若对于每一个$ k\;(3\leqslant k\leqslant n) $, 图$ G $都含有$ k $-圈, 则称图$ G $为泛圈图. 泛圈图是圈理论研究中的重要课题. 研究得到了Hamilton圈上两个不相邻的点在圈上的距离是3的泛圈性结果.

关键词: Hamilton图; 泛圈图;

本文引用格式

李静云 , 任韩 . 关于Hamilton图的新的圈结构定理[J]. 华东师范大学学报(自然科学版), 2020 , 2020(4) : 45 -50 . DOI: 10.3969/j.issn.1000-5641.201911013

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.

参考文献

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[5] 刘少强, 陈锦丽. (3)-泛圈图的一些必要条件 [J]. 闽南师范大学学报, 2014, 27(1): 7-15
[6] 陈耀静. (4)-泛圈图的一个必要条件 [J]. 闽南师范大学学报, 2019, 32(1): 10-20
[7] SCHMEICHEL E F, HAKIMI S L. A cycle structure theorem for Hamiltonian graphs [J]. Combin Theory (B), 1988, 45(1): 99-107. DOI: 10.1016/0095-8956(88)90058-5.
[8] REN H. Another cycle structure theorem for Hamiltonian graphs [J]. Discrete Mathematics, 1999, 199(1/2/3): 237-243.
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