Decompositions of Edge-Colored Complete Graphs

Abstract

We prove an asymptotic existence theorem for decompositions of edge-colored complete graphs into prespecified edge-colored subgraphs. Many combinatorial design problems fall within this framework. Applications of our main theorem require calculations involving the numbers of edges of each color and degrees of each color class of edges for the graphs allowed in the decomposition. We do these calculations to provide new proofs of the asymptotic existence of resolvable designs, near resolvable designs, group divisible designs, and grid designs. Two further applications are the asymptotic existence of skew Room d-cubes and the asymptotic existence of (v,k,1)-BIBDs with any group of order k - 1 as an automorphism group. © 2000 Academic Press.