Titlebook: A Course in Combinatorics and Graphs; Simeon Ball,Oriol Serra Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclusi

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978-3-031-55383-7The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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A Course in Combinatorics and Graphs978-3-031-55384-4Series ISSN 2296-4568 Series E-ISSN 2296-455X

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Introduction: Africa and the World, connections in other areas of combinatorics and of combinatorial optimization, besides its relevance in graph theory itself. Some structural results related to connectivity are also presented in this chapter, including a theorem of Tutte on 3-connected graphs. The close notion of edge-connectivity is also discussed at the end of the chapter.

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Simeon Ball,Oriol SerraCarefully crafted exercises for each chapter pitched to the right level of difficulty.Proofs are accompanied by exact copies of the figures we draw on the blackboard to explain the proofs.Hints and so

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https://doi.org/10.1007/978-3-031-21283-3ethod which provides a simple systematic way of obtaining the generating function of a class of combinatorial objects by a symbolic description of the class. Generating functions can be thought of as analytic complex functions or can be viewed simply as formal power series, by disregarding convergen

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https://doi.org/10.1007/978-3-031-21283-3elled objects. But imagine we wanted to count unlabelled objects, the number of graph on . vertices, for example. This is somewhat complicated by the fact that one has to ascertain when two graph are essentially the same. That is, there is a bijective map from the vertices of one to the vertices of

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Introduction: Africa and the World,e popular Soduku puzzles. As we shall prove in this chapter, there are a very large number of . latin squares. There are however, very few sets of mutually orthogonal latin squares. The problem of finding two mutually orthogonal latin squares can be rephrased in natural terms as the problem of linin

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African Development and Global Engagementsmpatible and cannot, for some reason, share a hotel room. Is it possible to find a solution to this problem? In terms of graphs, this is the matching problem, asking if there is a perfect matching of a given graph. In this chapter, we shall study matchings and prove Tutte’s theorem, which proves tha