Contractible cycles in graphs with large minimum degree Original Research Article

We show that if k ≥ 2 and G is a k-connected graph with minimum degree at least [3k/2], then, unless 2 ⩽ k ⩽ 3 and G is a complete graph on k + 2 vertices, G contains an induced cycle C such that G − V(C) is (k − 1)-connected.