Vertices of Degree 5 in a Contraction Critically 5-connected Graph

被引：1
|
作者：
Kiyoshi Ando
Atsushi Kaneko
Ken-ichi Kawarabayashi
机构：
[1] The University of Electro-Communications,Department of Information and Communication Engineering
[2] Kogakuin University,Department of Computer Science and Communication Engineering
[3] Tohoku University,Graduate School of Information Sciences
来源：
Graphs and Combinatorics | 2005年 / 21卷
关键词：
5-Connected graph; Contractible edge; Contraction critically ; -connected; 05C40;
D O I：
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学科分类号：
摘要：
An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is said to be contraction critically k-connected. We prove that a contraction critically 5-connected graph on n vertices has at least n/5 vertices of degree 5. We also show that, for a graph G and an integer k greater than 4, there exists a contraction critically k-connected graph which has G as its induced subgraph.
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页码：27 / 37
页数：10
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