Titlebook: One-Factorizations; W. D. Wallis Book 1997 Springer Science+Business Media Dordrecht 1997 Matching.graph theory.graphs.mathematics.combina

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Walks, Paths and Cycles,. A . is a walk in which no edge is repeated. A . is a walk in which no vertex is repeated; the . of a path is its number of edges. A walk is . when the first and last vertices, .. and .., are equal. A . of length . is a closed simple walk of length ., . ≥ 3, in which the vertices .., .., ..., x. are all different.

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Graphs,Any reader of this book will have some acquaintance with graph theory. However it seems advisable to have an introductory chapter, not only for completeness, but also because writers in this area differ on fundamental definitions: it is necessary to establish our version of the terminology.

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One-Factors and One-Factorizations,If . is any graph, then a . or . of . is a subgraph with vertex-set . (.). A . of . is a set of factors of . which are pairwise . no two have a common edge —and whose union is all of ..

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Orthogonal One-Factorizations,There are a number of applications of one-factorizations in the theory of combinatorial designs. In general this topic is too big to discuss here, but we shall explore a couple of examples. In this chapter we look at the applications concerning Latin squares; one-factorizations and block designs are discussed in Chapter 9.