DEGREE CONDITIONS FOR 2-FACTORS

For any positive integer k, we investigate degree conditions implying that a graph G of order n contains a 2-factor with exactly k component s (vertex disjoint cycles). In particular, we prove that for k less th an or equal to (n/4), Ore's classical condition for, a graph to be ham iltonian (k = 1) implies that the graph contains a 2-factor with exact ly Ic components. We also obtain a sufficient degree condition for a g raph to have k vertex disjoint cycles, at least s of which are 3-cycle s and the remaining are 4-cycles for any s less than or equal to k. (C ) 1997 John Wiley & Sons, Inc.