On a conjecture of bondy

Bondy conjectured 1] that: if G is a k-connected graph, where k ≥ 2, such that the degree-sum of any k + 1 independent vertices is at least m, then G contains a cycle of length at least: $\text{Min}\text{(}\text{2m}\text{(k + 1)}\text{, n)}$ (n denotes the order of G). We prove here that this result is true.