Abstract
Abstract An edge of a k -connected graph is said to be k -contractible if the contraction of the edge results in a k -connected graph. In this paper, we prove that a ( K 1 + C 4 )-free minimally k -connected graph has a k -contractible edge, if around each vertex of degree k , there is an edge which is not contained in a triangle. This implies previous two results, one due to Thomassen and the other due to Kawarabayashi.
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