Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path

L. Xiong; H.J. Broersma; C. Hoede

Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path

L. Xiong, H.J. Broersma, C. Hoede

Discrete Mathematics and Mathematical Programming

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Abstract

A graph is called {\sl subpancyclic} if it contains a cycle of length $l$ for each $l$ between 3 and the circumference of a graph. We show that if $G$ is a connected graph on $n\geq 146$ vertices such that $d(u)+d(v)+d(x)+d(y)>\frac{n+10}{2}$ for all four $u, v, x, y$ of a path $P=uvxy$ in $G, $ then its line graph is subpancyclic unless $G$ is isomorphic to an exceptional graph, and the result is best possible, even under the condition that $L(G)$ is hamiltonian.

Original language	English
Place of Publication	Enschede
Publisher	University of Twente, Department of Applied Mathematics
Number of pages	13
Publication status	Published - 2001

Publication series

Name	Memorandum
Publisher	Department of Applied Mathematics, University of Twente
No.	1606
ISSN (Print)	0169-2690

Keywords

MSC-05C45
IR-65793
EWI-3426
MSC-05C35

Access to Document

1606
open

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Xiong, L., Broersma, H. J., & Hoede, C. (2001). Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path. (Memorandum; No. 1606). Enschede: University of Twente, Department of Applied Mathematics.

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title = "Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path",

abstract = "A graph is called {\sl subpancyclic} if it contains a cycle of length $l$ for each $l$ between 3 and the circumference of a graph. We show that if $G$ is a connected graph on $n\geq 146$ vertices such that $d(u)+d(v)+d(x)+d(y)>\frac{n+10}{2}$ for all four $u, v, x, y$ of a path $P=uvxy$ in $G, $ then its line graph is subpancyclic unless $G$ is isomorphic to an exceptional graph, and the result is best possible, even under the condition that $L(G)$ is hamiltonian.",

keywords = "MSC-05C45, IR-65793, EWI-3426, MSC-05C35",

author = "L. Xiong and H.J. Broersma and C. Hoede",

note = "Imported from MEMORANDA",

year = "2001",

language = "English",

series = "Memorandum",

publisher = "University of Twente, Department of Applied Mathematics",

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T1 - Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path

AU - Xiong, L.

AU - Broersma, H.J.

AU - Hoede, C.

N1 - Imported from MEMORANDA

PY - 2001

Y1 - 2001

N2 - A graph is called {\sl subpancyclic} if it contains a cycle of length $l$ for each $l$ between 3 and the circumference of a graph. We show that if $G$ is a connected graph on $n\geq 146$ vertices such that $d(u)+d(v)+d(x)+d(y)>\frac{n+10}{2}$ for all four $u, v, x, y$ of a path $P=uvxy$ in $G, $ then its line graph is subpancyclic unless $G$ is isomorphic to an exceptional graph, and the result is best possible, even under the condition that $L(G)$ is hamiltonian.

AB - A graph is called {\sl subpancyclic} if it contains a cycle of length $l$ for each $l$ between 3 and the circumference of a graph. We show that if $G$ is a connected graph on $n\geq 146$ vertices such that $d(u)+d(v)+d(x)+d(y)>\frac{n+10}{2}$ for all four $u, v, x, y$ of a path $P=uvxy$ in $G, $ then its line graph is subpancyclic unless $G$ is isomorphic to an exceptional graph, and the result is best possible, even under the condition that $L(G)$ is hamiltonian.

KW - MSC-05C45

KW - IR-65793

KW - EWI-3426

KW - MSC-05C35

M3 - Report

T3 - Memorandum

BT - Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -