A new cycle structure theorem for Hamiltonian graphs

LI Jingyun; REN Han

doi:10.3969/j.issn.1000-5641.201911013

Issue 4

Jul. 2020

Turn off MathJax

Article Contents

Article Navigation > Journal of East China Normal University (Natural Sciences) > 2020 > (4): 45-50

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

Citation:

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

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

Citation:

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

PDF( 869 KB)

A new cycle structure theorem for Hamiltonian graphs

doi: 10.3969/j.issn.1000-5641.201911013

LI Jingyun^{1, 2},
REN Han^{1
,
,}

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
Available Online: 2020-07-20
Publish Date: 2020-07-20

Abstract

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.
- Hamiltonian graph,
- pancyclic graph,
- cycle

FullText(HTML)

References(8)

References

[1]	BONDY J A, MURTY U S R. Graph Theory with Applications [M]. New York: Macmilan Ltd Press, 1976.
[2]	BONDY J A. Pancyclic graphs I [J]. Combin Theory (B), 1971, 11(1): 80-84. DOI: 10.1016/0095-8956(71)90016-5.
[3]	ZHAO K W, LIN Y, ZHANG P. A sufficient condition for pancyclic graphs [J]. Information Processing Letters, 2009, 109(17): 991-996. DOI: 10.1016/j.ipl.2009.05.009.
[4]	ZAMFIRESCU C T. (2)-Pancyclic graphs [J]. Discrete Mathematics, 2013, 161(7/8): 1128-1136.
[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.