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 \(|V(G)| \geq 4k\). 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.