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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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