H-factors in dense graphs

Abstract

The following asymptotic result is proved. For every ε > 0, and for every positive integer h, there exists an n0 = n0(ε, h) such that for every graph H with h vertices and for every n>n0, any graph G with hn vertices and with minimum degree d≥((x(H) - 1)/x(H) +ε) hn contains n vertex disjoint copies of H. This result is asymptotically tight and its proof supplies a polynomial time algorithm for the corresponding algorithmic problem. © 1996 Academic Press, Inc.