On Vertex-Disjoint Chorded Cycles and Degree Sum Conditions

In this paper, we consider a degree sum condition sufficient to imply the existence of k vertex-disjoint chorded cycles in a graph G . Let σ 4 ( G ) be the minimum degree sum of four independent vertices of G . We prove that if G is a graph of order at least 11 k + 7 and σ 4 ( G ) ≥ 12 k − 3 with k ≥ 1 , then G contains k vertex-disjoint chorded cycles. We also show that the degree sum condition on σ 4 ( G ) is sharp.