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Traversing Graphs: The Eulerian and Hamiltonian Theme

  • Chapter
Arc Routing

Abstract

This chapter deals with basic graph theoretical concepts and then focuses on special topics which are — in their applications — of relevance to theoretical and practical problems in OR. Therefore, this chapter is structured as follows:

  1. 1.

    Basics of Graph Theory.

  2. 2.

    Connectivity, Menger’s Theorem, the Splitting Lemma, and Factors.

  3. 3.

    Eulerian Graphs and Covering Walks, Cycle Decompositions and Cycle Covers.

  4. 4.

    Hamiltonian Cycles and Vertex-Covering Walks.

  5. 5.

    Elements of Matching Theory.

  6. 6.

    The Chinese Postman Problem, The Traveling Salesman Problem, and Related Problems.

  7. 7.

    Elements of Network Theory.

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Author information

Authors and Affiliations

  1. Institute for Discrete Mathematics, Austrian Academy of Sciences, Austria

    Herbert Fleischner

Authors
  1. Herbert Fleischner
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Editor information

Editors and Affiliations

  1. Department of Management Information Systems, University of Arizona, Tucson, Arizona, 85721, USA

    Moshe Dror

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© 2000 Springer Science+Business Media New York

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Fleischner, H. (2000). Traversing Graphs: The Eulerian and Hamiltonian Theme. In: Dror, M. (eds) Arc Routing. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4495-1_2

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  • DOI: https://doi.org/10.1007/978-1-4615-4495-1_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7026-0

  • Online ISBN: 978-1-4615-4495-1

  • eBook Packages: Springer Book Archive

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