Contractible edges in k-connected graphs with minimum degree greater than or equal to [formula omitted

Abstract

Let G be a k-connected graph. An edge of G is said to be a k-contractible edge if the contraction of it results in a k-connected graph. Let Ec(G) denote the set of k-contractible edges of G. Let V(G) and δ(G) denote the set of vertices of G and the minimum degree of G, respectively. We prove that if k≥3, |V(G)|≥2k+1 and δ(G)≥⌊3k−12⌋, then |Ec(G)|≥|V(G)|+⌊5k−52⌋⌈k2⌉−k. We also show that this result is sharp.