| Longest Cycles in 2-Connected Quasi-Claw-Free Graphs |
| Received:June 04, 2012 Revised:July 07, 2013 |
| Key Words:
quasi-claw-free graph claw-free graph.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.60673046). |
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| Abstract: |
| A graph $G$ is called quasi-claw-free if it satisfies the property: $d(x,y)=2\Rightarrow$ there exists a vertex $u\in N(x)\cap N(y)$ such that $N[u]\subseteq N[x]\cup N[y]$. In this paper, we show that every 2-connected quasi-claw-free graph of order $n$ with $G\notin \mathcal{F}$ contains a cycle of length at least min$\{3\delta+2,n\}$, where $\mathcal{F}$ is a family of graphs. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.01.003 |
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