Degree sums and subpancyclicity in line graphs

Liming Xiong; H. J. Broersma; C. Hoede; Xueliang Li

doi:10.1016/S0012-365X(00)00468-4

Degree sums and subpancyclicity in line graphs

Liming Xiong
, H. J. Broersma
, C. Hoede
, Xueliang Li

Jiangxi Normal University
University of Twente
Northwestern Polytechnical University Xian

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

A graph is called subpancyclic if it contains a cycle of length k for each k between 3 and the circumference of the graph. In this paper, we show that if the degree sum of the vertices along each 2-path of a graph G exceeds (n + 6)/2, or if the degree sum of the vertices along each 3-path of G exceeds (2n + 16)/3, then its line graph L(G) is subpancyclic. Simple examples show that these bounds are best possible. Our results shed some light on the content of a famous Metaconjecture of Bondy.

源语言	英语
页（从-至）	255-267
页数	13
期刊	Discrete Mathematics
卷	242
期	1-3
DOI	https://doi.org/10.1016/S0012-365X(00)00468-4
出版状态	已出版 - 1 6月 2002
已对外发布	是

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abstract = "A graph is called subpancyclic if it contains a cycle of length k for each k between 3 and the circumference of the graph. In this paper, we show that if the degree sum of the vertices along each 2-path of a graph G exceeds (n + 6)/2, or if the degree sum of the vertices along each 3-path of G exceeds (2n + 16)/3, then its line graph L(G) is subpancyclic. Simple examples show that these bounds are best possible. Our results shed some light on the content of a famous Metaconjecture of Bondy.",

keywords = "Degree sum, Line graph, Path, Subpancyclicity",

author = "Liming Xiong and Broersma, \{H. J.\} and C. Hoede and Xueliang Li",

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T1 - Degree sums and subpancyclicity in line graphs

AU - Xiong, Liming

AU - Broersma, H. J.

AU - Hoede, C.

AU - Li, Xueliang

PY - 2002/6/1

Y1 - 2002/6/1

N2 - A graph is called subpancyclic if it contains a cycle of length k for each k between 3 and the circumference of the graph. In this paper, we show that if the degree sum of the vertices along each 2-path of a graph G exceeds (n + 6)/2, or if the degree sum of the vertices along each 3-path of G exceeds (2n + 16)/3, then its line graph L(G) is subpancyclic. Simple examples show that these bounds are best possible. Our results shed some light on the content of a famous Metaconjecture of Bondy.

AB - A graph is called subpancyclic if it contains a cycle of length k for each k between 3 and the circumference of the graph. In this paper, we show that if the degree sum of the vertices along each 2-path of a graph G exceeds (n + 6)/2, or if the degree sum of the vertices along each 3-path of G exceeds (2n + 16)/3, then its line graph L(G) is subpancyclic. Simple examples show that these bounds are best possible. Our results shed some light on the content of a famous Metaconjecture of Bondy.

KW - Degree sum

KW - Line graph

KW - Path

KW - Subpancyclicity

UR - https://www.scopus.com/pages/publications/33646070633

U2 - 10.1016/S0012-365X(00)00468-4

DO - 10.1016/S0012-365X(00)00468-4

M3 - Article

AN - SCOPUS:33646070633

SN - 0012-365X

VL - 242

SP - 255

EP - 267

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

Degree sums and subpancyclicity in line graphs

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