Contractible edges in k-connected graphs with minimum degree greater than or equal to left perpendicular 3k-1/2 right perpendicular

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 E-c(G) denote the set of k-contractible edges of G. Let V(G) and delta(G) denote the set of vertices of G and the minimum degree of G, respectively. We prove that if k >= 3, vertical bar V(G)vertical bar >= 2k + 1 and delta(G) >= left perpendicular 3k-1/2 right perpendicular, then vertical bar E-c(G)vertical bar >= vertical bar V(G)vertical bar + left perpendicular 5k-5/2 right perpendicular - k. We also show that this result is sharp. (C) 2021 Elsevier B.V. All rights reserved.