On regular embedding of H-designs into G-designs

Abstract

The graph H is embedded in the graph G, if H is a subgraph of G. An H-design is a decomposition of a complete graph into edge disjoint copies of the graph H, called blocks. An H-design with k blocks, say H1, H2, ...Hk is embedded in a G-design if for every Hi, there exists a distinct block, say Gi, in the G-design that embeds Hi. If Gi - Hi are all isomorphic for 1 ≤ i ≤ k then the embedding is called regular. This paper solves the problem of the regular embedding of H-designs into G-designs when G has at most four vertices and four edges.