Partitioning a graph into cycles with a specified number of chords

For a graph G , let σ 2 ( G ) be the minimum degree sum of two nonadjacent vertices in G . A chord of a cycle in a graph G is an edge of G joining two nonconsecutive vertices of the cycle. In this paper, we prove the following result, which is an extension of a result of Brandt et al for large graphs: For positive integers k and c , there exists an integer f ( k , c ) such that if G is a graph of order n ≥ f ( k , c ) and σ 2 ( G ) ≥ n , then G can be partitioned into k vertex‐disjoint cycles, each of which has at least c chords.