Summary: Almost H-factors in dense graphs
and Raphael Yuster
Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
The following asymptotic result is proved. For every fixed graph H with h vertices, any
graph G with n vertices and with minimum degree d (H)-1
(H) n contains (1 - o(1))n/h vertex
disjoint copies of H.
Research supported in part by a United States Israel BSF Grant and by a Bergmann Memorial Grant
All graphs considered here are finite, undirected and simple (i.e., have no loops and no parallel
edges). If G is a graph on n vertices and H is a graph on h vertices, we say that G has an H-factor
if it contains n/h vertex disjoint copies of H. Thus, for example, a K2-factor is simply a perfect
matching, whereas a C4-factor is a spanning subgraph of G every connected component of which
is a cycle of length 4.