Pancyclicity of 4-Connected {Claw, Generalized Bull}-Free Graphs

Authors

Michael Ferrara, University of Colorado DenverFollow
Silke Gehrke, Emory University
Ronald Gould, Emory UniversityFollow
Colton Magnant, Georgia Southern UniversityFollow
Jeffrey Powell, Samford University

Document Type

Article

Publication Date

2-28-2013

Publication Title

Discrete Mathematics

DOI

10.1016/j.disc.2012.11.015

ISSN

0012-365X

Abstract

A graph G is pancyclic if it contains cycles of each length ℓ, 3≤ℓ≤|V(G)|. The generalized bull B(i,j) is obtained by associating one endpoint of each of the paths P_i+1 and P_j+1 with distinct vertices of a triangle. Gould, Łuczak and Pfender (2004) [4] showed that if G is a 3-connected {K_1,3,B(i,j)}-free graph withi+j=4 then G is pancyclic. In this paper, we prove that every 4-connected, claw-free, B(i,j)-free graph with i+j=6 is pancyclic. As the line graph of the Petersen graph is B(i,j)-free for any i+j=7 and is not pancyclic, this result is best possible.

Recommended Citation

Ferrara, Michael, Silke Gehrke, Ronald Gould, Colton Magnant, Jeffrey Powell. 2013. "Pancyclicity of 4-Connected {Claw, Generalized Bull}-Free Graphs." Discrete Mathematics, 303 (4): 460-467. doi: 10.1016/j.disc.2012.11.015
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/103