 
Summary: Threshold functions for Hfactors
Noga Alon
Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
and
Raphael Yuster
Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
Abstract
Let H be a graph on h vertices, and let G be a graph on n vertices. An Hfactor of
G is a spanning subgraph of G consisting of n/h vertex disjoint copies of H. The fractional
arboricity of H is a(H) = max{ E 
V 1 }, where the maximum is taken over all subgraphs (V , E )
of H with V  > 1. Let (H) denote the minimum degree of a vertex of H. It is shown
that if (H) < a(H) then n1/a(H)
is a sharp threshold function for the property that the
random graph G(n, p) contains an Hfactor. I.e., there are two positive constants c and C so
that for p(n) = cn1/a(H)
