Abstract:  

Let v >= k and m be positive integers.  A block design BD(v,k,m) is a collection A of k-subsets 
of a v-set X in which every unordered pair of elements from X is contained  in exactly m elements of A.  
More generally, for a fixed simple graph G, a graph design GD(v,G,m) is a collection A of graphs isomorphic 
to G with vertices in X such that every unordered pair of elements from X is an edge of exactly m elements 
of A.  A famous result of Wilson says that for a fixed G and m, there exists a GD(v,G,m) for all sufficiently large 
v satisfying certain necessary conditions.  A block (graph) design as above is said to be resolvable if A can be 
partitioned into partitions of (graphs whose vertex sets partition) X. Lu has shown asymptotic existence of resolvable
 BD(v,k,m), yet for over twenty years the analogous problem for resolvable GD(v,k,m) has remained open.  In this
 paper, we settle asymptotic existence of resolvable graph designs.