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.

16 pages, 2 figures