Embedding Partial k ‐Star Designs

A k ‐star is the complete bipartite graph K 1 , k . Let G and H be graphs, and let B be a partial H ‐decomposition of G . A partial H ‐decomposition, B ′ , of another graph G ′ is called an embedding of B provided that B ⊆ B ′and G is a subgraph of G ′ . We find an embedding of a partial k ‐star decomposition of K n into a k ‐star decomposition of K n + s , where s is at most 7 k − 4 if k is odd, and 8 k − 4 if k is even.