Proof of a conjecture of Häggkvist on cycles and independent edges

A graph G of order n is a c"k-graph if for every pair of distinct, nonadjacent vertices x and y: d(x) + d(y) >= n + k where d(@n) denotes the degree of a vertex @n. In this paper, we prove the conjecture of Haggkvist [4] which states that every set of independent edges of a c"1-graph is contained in a cycle.