Nonseparating cycles in K ‐Connected graphs
Carsten Thomassen · Journal of Graph Theory · 1981
Abstract We show that every k ‐connected graph with no 3‐cycle contains an edge whose contraction results in a k ‐connected graph and use this to prove that every ( k + 3)‐connected graph contains a cycle whose deletion results in a k ‐connected graph. This settles a problem of L. Lovász.