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- W2103437676 abstract "Let $K(a^{(p)};lambda,mu )$ be a graph with $p$ parts, each part having size $a$, in which the multiplicity of each pair of vertices in the same part (in different parts) is $lambda$ ($mu $, respectively). In this paper we consider the following embedding problem: When can a graph decomposition of $K(a^{(p)};lambda,mu )$ be extended to a Hamiltonian decomposition of $K(a^{(p+r)};lambda,mu )$ for $r>0$? A general result is proved, which is then used to solve the embedding problem for all $rgeq frac{lambda}{mu a}+frac{p-1}{a-1}$. The problem is also solved when $r$ is as small as possible in two different senses, namely when $r=1$ and when $r=frac{lambda}{mu a}-p+1$." @default.
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- W2103437676 date "2012-04-12" @default.
- W2103437676 modified "2023-10-18" @default.
- W2103437676 title "Embedding an Edge-colored K(a (p); λ, μ) into a Hamiltonian Decomposition of K(a (p+r); λ, μ)" @default.
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- W2103437676 doi "https://doi.org/10.1007/s00373-012-1164-0" @default.
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