Maximum number of edges in a critically k-connected graph Original Research Article

A k-connected graph G is said to be critically k-connected if G−v is not k-connected for any v∈V(G). We show that if n,k are integers with k⩾4 and n⩾k+2, and G is a critically k-connected graph of order n, then |E(G)|⩽n(n−1)/2−p(n−k)+⌊p2/2⌋, where p=(n/k)+1 if n/k is an odd integer and p=⌈n/k⌉ otherwise. We also characterize extremal graphs.