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The contractible subgraph of $5$ -connected graphs

Chengfu Qin; Xiaofeng Guo; Weihua Yang — 2013

Czechoslovak Mathematical Journal

An edge $e$ of a $k$ -connected graph $G$ is said to be $k$ -removable if $G - e$ is still $k$ -connected. A subgraph $H$ of a $k$ -connected graph is said to be $k$ -contractible if its contraction results still in a $k$ -connected graph. A $k$ -connected graph with neither removable edge nor contractible subgraph is said to be minor minimally $k$ -connected. In this paper, we show that there is a contractible subgraph in a $5$ -connected graph which contains a vertex who is not contained in any triangles. Hence, every vertex of minor...

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The contractible subgraph of 5 -connected graphs

The contractible subgraph of $5$ -connected graphs