Embedding Partial k-Star Designs



A k-star is the complete bipartite graph inline image. Let G and H be graphs, and let inline image be a partial H-decomposition of G. A partial H-decomposition, inline image, of another graph inline image is called an embedding of inline image provided that inline image and G is a subgraph of inline image. We find an embedding of a partial k-star decomposition of inline image into a k-star decomposition of inline image, where s is at most inline image if k is odd, and inline image if k is even.