On \(2\)-Factors with Chorded Quadrilaterals in Graphs

Abstract

Let \(k\) be a positive integer and \(G\) a graph with order \(n \geq 4k + 3\). It is proved that if the minimum degree sum of any two nonadjacent vertices is at least \(n + k\), then \(G\) contains a 2-factor with \(k + 1\) disjoint cycles \(C_1, \ldots, C_{k+1}\) such that \(C_i\) are chorded quadrilaterals for \(1 \leq i \leq k-1\) and the length of \(C_{k}\) is at most \(4\).