Topics in Matroid Theory

  • Leonidas S.┬áPitsoulis
Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Leonidas Pitsoulis
    Pages 1-4
  3. Leonidas Pitsoulis
    Pages 5-24
  4. Leonidas Pitsoulis
    Pages 25-45
  5. Leonidas Pitsoulis
    Pages 75-100
  6. Leonidas Pitsoulis
    Pages 101-120
  7. Back Matter
    Pages 121-127

About this book

Introduction

Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides  a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.  

Keywords

combinatorial geometries combinatorial optimization matroid theory recognition algorithm union algorithms

Authors and affiliations

  • Leonidas S.┬áPitsoulis
    • 1
  1. 1.Dept. of Mathematical & Physical Sci.Aristotle University of Thessaloniki School of EngineeringThessalonikiGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-8957-3
  • Copyright Information Leonidas S. Pitsoulis 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-8956-6
  • Online ISBN 978-1-4614-8957-3
  • Series Print ISSN 2190-8354
  • Series Online ISSN 2191-575X
  • About this book