# Pancyclicity of 4-Connected Claw-free Net-free Graphs

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Mingquan Zhan

Millersville University of Pennsylvania

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**Minisymposium:**
GENERAL SESSION TALKS

**Content:**
A graph $G$ is said to be pancyclic if $G$ contains cycles of lengths from 3 to $|V(G)|$. The net $B(i,j)$ is obtained by associating one endpoint of each of the path $P_{i+1}$ and $P_{j+1}$ with distinct vertices of a triangle. Ferrara et al. (2013) \cite{FGGMP2013} showed that every 4-connected $\{K_{1,3},B(i,j)\}$-free graph with $i+j=6$ is pancyclic. In this paper we show that every 4-connected $\{K_{1,3}, B(i,j)\}$-free graph with $i+j=7$ is either pancyclic or it is the line graph of the Petersen graph.