Abstract :
It is proved that a graph with n vertices and minimum degree at least [(h + 2)/2h]n contains n/h−O(h2) vertex disjoint cycles of size h, and that a graph with n > N(h) vertices and minimum degree at least [(h + 3)/2h]n contains n/h vertex disjoint h-cycles, provided h divides n. Bounds on the minimum degree required for G to contain a factor consisting of cycles of specified lengths are also discussed. This work is motivated by a conjecture of El-Zahar (1984).
