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Matroid Theory and its Applications in Electric Network Theory and in Statics

  • Book
  • © 1989

Overview

Authors:
  1. András Recski

    1. Eötvös Loránd University, Budapest VIII, Hungary

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Part of the book series: Algorithms and Combinatorics (AC, volume 6)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Part One

    1. Front Matter

      Pages 1-1
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    2. Basic concepts from graph theory

      • András Recski
      Pages 3-36

    3. Applications

      • András Recski
      Pages 37-68

    4. Planar graphs and duality

      • András Recski
      Pages 69-91

    5. Applications

      • András Recski
      Pages 92-106

    6. The theorems of König and Menger

      • András Recski
      Pages 107-130

    7. Applications

      • András Recski
      Pages 131-147

  3. Part Two

    1. Front Matter

      Pages 149-149
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    2. Basic concepts in matroid theory

      • András Recski
      Pages 151-170

    3. Applications

      • András Recski
      Pages 171-184

    4. Algebraic and geometric representation of matroids

      • András Recski
      Pages 185-205

    5. Applications

      • András Recski
      Pages 206-221

    6. The sum of matroids I

      • András Recski
      Pages 222-232

    7. Applications

      • András Recski
      Pages 233-246

    8. The sum of matroids II

      • András Recski
      Pages 247-259

    9. Applications

      • András Recski
      Pages 260-272

    10. Matroids induced by graphs

      • András Recski
      Pages 273-286

    11. Applications

      • András Recski
      Pages 287-292

    12. Some recent results in matroid theory

      • András Recski
      Pages 293-306
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Keywords

About this book

I. The topics of this book The concept of a matroid has been known for more than five decades. Whitney (1935) introduced it as a common generalization of graphs and matrices. In the last two decades, it has become clear how important the concept is, for the following reasons: (1) Combinatorics (or discrete mathematics) was considered by many to be a collection of interesting, sometimes deep, but mostly unrelated ideas. However, like other branches of mathematics, combinatorics also encompasses some gen­ eral tools that can be learned and then applied, to various problems. Matroid theory is one of these tools. (2) Within combinatorics, the relative importance of algorithms has in­ creased with the spread of computers. Classical analysis did not even consider problems where "only" a finite number of cases were to be studied. Now such problems are not only considered, but their complexity is often analyzed in con­ siderable detail. Some questions of this type (for example, the determination of when the so called "greedy" algorithm is optimal) cannot even be answered without matroidal tools.

Authors and Affiliations

  • Eötvös Loránd University, Budapest VIII, Hungary

    András Recski

Bibliographic Information

  • Book Title: Matroid Theory and its Applications in Electric Network Theory and in Statics

  • Authors: András Recski

  • Series Title: Algorithms and Combinatorics

  • DOI: https://doi.org/10.1007/978-3-662-22143-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-662-22145-7Published: 03 October 2013

  • eBook ISBN: 978-3-662-22143-3Published: 29 June 2013

  • Series ISSN: 0937-5511

  • Series E-ISSN: 2197-6783

  • Edition Number: 1

  • Number of Pages: XIII, 533

  • Additional Information: Jointly published with Akademiai Kiado, Budapest, Hungary

  • Topics: Combinatorics, Geometry, Topology, Mathematical and Computational Engineering, Electrical Engineering

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