On the number of contractible triples in 3-connected graphs

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• 作者：Matthias Kriesell
• 关键词：Connectivity ; Contractible edge ; Contractible triple
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2008
• 出版时间：January 2008
• 年：2008
• 卷：98
• 期：1
• 页码：136-145
• 全文大小：162 K

文摘

McCuaig and Ota proved that every 3-connected graph G on at least 9 vertices admits a contractible triple, i.e. a connected subgraph H on three vertices such that G−V(H) is 2-connected. Here we show that every 3-connected graph G on at least 9 vertices has more than |V(G)|/10 many contractible triples. If, moreover, G is cubic, then there are at least |V(G)|/3 many contractible triples, which is best possible.