| 2-连通半无爪图的最长圈 |
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| 引用本文： | 陈晓东,李明楚,马欣.2-连通半无爪图的最长圈[J].数学研究及应用,2014,34(1):33-42. |
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| 作者姓名： | 陈晓东 李明楚 马欣 |
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| 作者单位： | 辽宁工业大学数学学院, 辽宁 沈阳 121001;大连理工大学软件学院, 辽宁 大连 116024;沈阳建筑大学城市学院, 辽宁 大连 110167 |
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| 基金项目： | 国家自然科学基金(Grant No.60673046). |
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| 摘 要： | A graph G is called quasi-claw-free if it satisfies the property:d(x,y)=2 there exists a vertex u∈N(x)∩N(y)such that Nu]■Nx]∪Ny].In this paper,we show that every 2-connected quasi-claw-free graph of order n with G■F contains a cycle of length at least min{3δ+2,n},where F is a family of graphs.
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| 关 键 词： | 半无爪图 连通 最长圈 顶点 周期 |
| 收稿时间： | 6/4/2012 12:00:00 AM |
| 修稿时间： | 7/7/2013 12:00:00 AM |
Longest Cycles in 2-Connected Quasi-Claw-Free Graphs |
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| Xiaodong CHEN,Mingchu LI and Xin MA.Longest Cycles in 2-Connected Quasi-Claw-Free Graphs[J].Journal of Mathematical Research with Applications,2014,34(1):33-42. |
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| Authors: | Xiaodong CHEN Mingchu LI and Xin MA |
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| Institution: | College of Science, Liaoning University of Technology, Liaoning 121001, P. R. China;School of Softsware, Dalian University of Technology, Liaoning 116024, P. R. China;Basic Science Department, Shenyang Urban Construction University, Liaoning 110167, P. R. China |
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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 $Nu]\subseteq Nx]\cup Ny]$. 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. |
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| Keywords: | quasi-claw-free graph claw-free graph |
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