Degree conditions for 2-factors

Abstract

For any positive integer k, we investigate degree conditions implying that a graph G of order n contains a 2-factor with exactly k components (vertex disjoint cycles). In particular, we prove that for k ≤ (n/4), Ore's classical condition for a graph to be hamiltonian (k = 1) implies that the graph contains a 2-factor with exactly k components. We also obtain a sufficient degree condition for a graph to have k vertex disjoint cycles, at least s of which are 3-cycles and the remaining are 4-cycles for any s ≤ k. © 1997 John Wiley & Sons, Inc.