The contractible subgraph of -connected graphs
Chengfu Qin, Xiaofeng Guo, Weihua Yang (2013)
Czechoslovak Mathematical Journal
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An edge of a -connected graph is said to be -removable if is still -connected. A subgraph of a -connected graph is said to be -contractible if its contraction results still in a -connected graph. A -connected graph with neither removable edge nor contractible subgraph is said to be minor minimally -connected. In this paper, we show that there is a contractible subgraph in a -connected graph which contains a vertex who is not contained in any triangles. Hence, every vertex...