@MISC{Kawarabayashi_noteon, author = {Ken-ichi Kawarabayashi}, title = {Note on k-contractible edges in k-connected graphs}, year = {} }

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Abstract

It is proved that if G is a k-connected graph which does not contain K;; with k being odd, then G has an edge e such that the graph obtained from G by contracting e is still k-connected. The same conclusion does not hold when k is even. This result is a generalization of the famous theorem of Thomassen [J. Graph Theory 5 (1981), 351--354] when k is odd. 1