On minimum embeddings of Pk(u, λ) into KS(u+w,μ)
Keywords:
graph decomposition, embedding, minimum embeddingAbstract
Let G be a simple finite graph and H be a subgraph of G. We say that an H-design (U,C) of order u and index λ is embedded into a G-design (V,B) of order u+w and index μ, λ ≤ μ, if there is an injective function f : C → B such that C is a subgraph of f (C) for every C ∈ C. The mapping f is called the embedding of (U,C) into (V,B). If w attains the minimum possible value, then f is a minimum embedding. In this paper we study the minimum embedding of a Pk(u,λ) into a KS(u+w,μ), for k = 3,4.
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