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Contractible edges in some k -connected graphs

Yingqiu YangLiang Sun — 2012

Czechoslovak Mathematical Journal

An edge e of a k -connected graph G is said to be k -contractible (or simply contractible) if the graph obtained from G by contracting e (i.e., deleting e and identifying its ends, finally, replacing each of the resulting pairs of double edges by a single edge) is still k -connected. In 2002, Kawarabayashi proved that for any odd integer k 5 , if G is a k -connected graph and G contains no subgraph D = K 1 + ( K 2 K 1 , 2 ) , then G has a k -contractible edge. In this paper, by generalizing this result, we prove that for any integer...

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