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Amalgamations of factorizations of complete graphs. (English) Zbl 1153.05055
Let \(K=(k_1,\ldots,k_t)\) and \(L=(l_1,\ldots,l_t)\) be collections of nonnegative integers. A factorization of a graph into factors \(F_1,\ldots,F_t\) is called a \((t,K,L)\)-factorization if each factor \(F_i\) is a \(k_i\)-regular \(l_i\)-connected graph. Johnstone in 2000 proved a necessary and sufficient condition for existence of a \((t,K,L)\)-factorization of a complete graph \(K_n\). In this paper the author gives another proof of this result using amalgamations. He also proves a necessary and sufficient condition for existence of an embedding of a factorization of \(K_m\) in a \((t,K,L)\)-factorization of \(K_n\).

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C40 Connectivity
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