On the Maximum Number of Disjoint Chorded Cycles in Graphs

Abstract

Let $k$ be a positive integer and let $G=(V(G),E(G))$ be a graph with $|V(G)|\ge 4k$. In this paper, it is proved that if the minimum degree sum is at least $6k–1$ for each pair of nonadjacent vertices in $V(G)$, then $G$ contains $k$ vertex-disjoint chorded cycles. This result generalizes the main Theorem of Finkel. Moreover, the degree condition is sharp in general.