Abstract

We combine two well-known results by Mader and Thomassen, respectively. Namely, we prove that for any k -connected graph G ( k ≥ 4 ), there is an induced cycle C such that G − V ( C ) is ( k − 3 ) -connected and G − E ( C ) is ( k − 2 ) -connected. Both “ ( k − 3 ) -connected” and “ ( k − 2 ) -connected” are best possible in a sense.

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