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Decompositions of complete graphs: Embedding partial edge-colourings and the method of amalgamations. (English) Zbl 1028.05083
Wensley, C. D. (ed.), Surveys in combinatorics, 2003. Proceedings of the 19th British combinatorial conference, University of Wales, Bangor, UK, June 29-July 04, 2003. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 307, 7-41 (2003).
In this survey paper, the authors consider decompositions of the edges of complete graphs, mainly with each part inducing a spanning subgraph with specified properties. They give special attention to embedding questions, where a decomposition of the edges of a complete subgraph of a complete graph is given, and the problem is to extend the decomposition to a full decomposition with the desired properties. One way to obtain decomposition and embedding results simultaneously is by the method of amalgamations of vertices, to which the authors devote a large part of their paper. The list of references contains 58 items.
For the entire collection see [Zbl 1020.00011].

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C10 Planar graphs; geometric and topological aspects of graph theory
05B15 Orthogonal arrays, Latin squares, Room squares