On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles

Abstract

In this paper, we consider a general degree sum condition sufficient to imply the existence of k vertex-disjoint chorded cycles in a graph G. Let $$\sigma _t(G)$$ be the minimum degree sum of t independent vertices of G. We prove that if G is a graph of sufficiently large order and $$\sigma _t(G)\ge 3kt-t+1$$ with $$k\ge 1$$ , then G contains k vertex-disjoint chorded cycles. We also show that the degree sum condition on $$\sigma _t(G)$$ is sharp. To do this, we also investigate graphs without chorded cycles.