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Contractible Cliques in k-Connected Graphs (2005)
by
Xiaolong Huang
,
Zemin Jin
,
Xingxing Yu
,
Xiaoyan Zhang
BibTeX
@MISC{Huang05contractiblecliques,
author = {Xiaolong Huang and Zemin Jin and Xingxing Yu and Xiaoyan Zhang},
title = {Contractible Cliques in k-Connected Graphs },
year = {2005}
}
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Abstract
Kawarabayashi proved that for any integer k ≥ 4, every k-connected graph contains two triangles sharing an edge, or admits a k-contractible edge, or admits a k-contractible triangle. This implies Thomassen’s result that every triangle-free k-connected graph contains a k-contractible edge. In this paper, we extend Kawarabayashi’s technique and prove a more general result concerning k-contractible cliques.
