| 几乎无爪图的叶子数较少的生成树 |
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| 引用本文： | 陈晓东,李明楚,徐美进.几乎无爪图的叶子数较少的生成树[J].数学研究及应用,2016,36(4):450-456. |
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| 作者姓名： | 陈晓东 李明楚 徐美进 |
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| 作者单位： | 辽宁工业大学理学院, 辽宁 锦州 121001,大连理工大学软件学院, 辽宁 116024,辽宁工业大学理学院, 辽宁 锦州 121001 |
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| 基金项目： | 国家自然科学基金数学天元基金项目(Grant No.11426125),辽宁省教育厅(Grant No.L2014239). |
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| 摘 要： | A spanning tree with no more than 3 leaves is called a spanning 3-ended tree.In this paper, we prove that if G is a k-connected(k ≥ 2) almost claw-free graph of order n and σ_(k+3)(G) ≥ n + k + 2, then G contains a spanning 3-ended tree, where σk(G) =min{∑_(v∈S)deg(v) : S is an independent set of G with |S| = k}.
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| 关 键 词： | spanning 3-ended tree almost claw-free graph insertible vertex non-insertible vertex |
| 收稿时间： | 2015/10/20 0:00:00 |
| 修稿时间： | 2016/4/15 0:00:00 |
Spanning Trees with Few Leaves in Almost Claw-Free Graphs |
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| Xiaodong CHEN,Mingchu LI and Meijin XU.Spanning Trees with Few Leaves in Almost Claw-Free Graphs[J].Journal of Mathematical Research with Applications,2016,36(4):450-456. |
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| Authors: | Xiaodong CHEN Mingchu LI and Meijin XU |
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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 and College of Science, Liaoning University of Technology, Liaoning 121001, P. R. China |
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| Abstract: | A spanning tree with no more than 3 leaves is called a spanning 3-ended tree. In this paper, we prove that if $G$ is a $k$-connected ($k\geq 2$) almost claw-free graph of order $n$ and $\sigma_{k+3}(G)\geq {n+k+2}$, then $G$ contains a spanning 3-ended tree, where $\sigma_k(G)=\min\{\sum_{v\in S}{\rm deg}(v):S$ is an independent set of $G$ with $|S|=k\}$. |
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| Keywords: | spanning 3-ended tree almost claw-free graph insertible vertex non-insertible vertex |
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