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

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

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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 Enschede University of Twente, Department of Applied Mathematics 13 Published - 2001

Publication series

Name Memorandum Department of Applied Mathematics, University of Twente 1606 0169-2690

Fingerprint

Degree Sum
Line Graph
Path
Graph in graph theory
Circumference
Connected graph
Isomorphic
Cycle

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

Cite this

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.
Xiong, L. ; Broersma, H.J. ; Hoede, C. / Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path. Enschede : University of Twente, Department of Applied Mathematics, 2001. 13 p. (Memorandum; 1606).
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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.",
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author = "L. Xiong and H.J. Broersma and C. Hoede",
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Xiong, L, Broersma, HJ & Hoede, C 2001, Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path. Memorandum, no. 1606, University of Twente, Department of Applied Mathematics, Enschede.
Enschede : University of Twente, Department of Applied Mathematics, 2001. 13 p. (Memorandum; No. 1606).

Research output: Book/ReportReportOther research output

TY - BOOK

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 -

Xiong L, Broersma HJ, Hoede C. Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path. Enschede: University of Twente, Department of Applied Mathematics, 2001. 13 p. (Memorandum; 1606).