#### Title

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

#### 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