Spanning 3-ended trees in k-connected K_(1,4)-free graphs  

作　　者：CHEN Yuan CHEN GuanTao HU ZhiQuan 

机构地区：[1]Faculty of Mathematics and Statistics, Central China Normal University [2]College of Mathematics and Computer Science, Wuhan Textile University [3]Department of Mathematics and Statistics, Georgia State University

出　　处：《Science China Mathematics》2014年第8期1579-1586,共8页中国科学：数学（英文版）

基　　金：supported by Scientific Research Fund of Hubei Provincial Education Department (Grant No. Q20141609);National Natural Science Foundation of China (Grant Nos. 11371162 and 11271149);Wuhan Textile University (2012)

摘　　要：A tree with at most m leaves is called an m-ended tree.Kyaw proved that every connected K1,4-free graph withσ4(G)n-1 contains a spanning 3-ended tree.In this paper we obtain a result for k-connected K1,4-free graphs with k 2.Let G be a k-connected K1,4-free graph of order n with k 2.Ifσk+3(G)n+2k-2,then G contains a spanning 3-ended tree.A tree with at most m leaves is called an m-ended tree. Kyaw proved that every connected K1,4-free graph with σ4（G） n-1 contains a spanning 3-ended tree. In this paper we obtain a result for k-connected K1,4-free graphs with k 2. Let G be a k-connected K1,4-free graph of order n with k 2. If σk＋3（G） n ＋ 2k- 2,then G contains a spanning 3-ended tree.

关 键 词：spanning tree degree sum insertible vertex segment insertion 

分 类 号：O157.5[理学—数学]