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Basic Terminology, Notation and Results

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Classes of Directed Graphs

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Abstract

In this chapter we will provide most of the terminology and notation used in this book. Various examples, figures and results should help the reader to better understand the notions introduced in the chapter. We also prove some basic results on digraphs and provide some fundamental digraph results without proofs. Most of our terminology and notation is standard and agrees with (Bang-Jensen, Gutin, Digraphs: theory, algorithms and applications. Springer, London, 2009, [4]).

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Notes

  1. 1.

    If we know from the context that D is directed, D may be called a graph.

  2. 2.

    By Menger’s theorem (Theorem 1.5.3), (1.1) is equivalent to the existence of k arc-disjoint dipaths from z to every other vertex of D.

  3. 3.

    The symmetric TSP is the problem of finding a minimum weight Hamilton cycle in a weighted complete undirected graph.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK5230, Odense M, Denmark

    Jørgen Bang-Jensen

  2. Department of Computer Science, Royal Holloway University, Egham Hill, TW20 0EX, Egham, England

    Gregory Gutin

Authors
  1. Jørgen Bang-Jensen
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  2. Gregory Gutin
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Correspondence to Gregory Gutin .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Jørgen Bang-Jensen

  2. Department of Computer Science, Royal Holloway, University of London, Egham, United Kingdom

    Gregory Gutin

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Bang-Jensen, J., Gutin, G. (2018). Basic Terminology, Notation and Results. In: Bang-Jensen, J., Gutin, G. (eds) Classes of Directed Graphs. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-71840-8_1

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