Contractible edges and triangles in k-connected graphs

被引：21
|
作者：
Kawarabayashi, K
机构：
[1] Keio Univ, Dept Math, Kohoku Ku, Yokohama, Kanagawa 2238522, Japan
[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2002年 / 85卷 / 02期
基金：
日本学术振兴会;
关键词：
contractible edges; triangles; cycles;
D O I：
10.1006/jctb.2001.2096
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is proved that if G is a k-connected graph which does not contain K-4(-), then G has an edge a or a triangle T such that the graph obtained from G by connecting e or by contracting T is still k-connected. By using this theorem, we prove some theorems which are generalizations of earlier work. In addition, we give a condition for a k-connected graph to have a k-contractible edge, which implies two theorems proved by C. Thomassen (1981, J. Graph Theory 5, 351-354) and by the author (2001, Australas. J. Combin. 24, 165-168). respectively. (C) 2002 Elsevier Science (USA).
引用
收藏
页码：207 / 221
页数：15
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