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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
##### Keywords:
factorizations; embeddings; amalgamations
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##### References:
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