Sparsity

Graphs, Structures, and Algorithms

  • Jaroslav Nešetřil
  • Patrice Ossona de Mendez

Part of the Algorithms and Combinatorics book series (AC, volume 28)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Presentation

    1. Front Matter
      Pages 1-1
    2. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 3-5
    3. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 7-17
  3. The Theory

    1. Front Matter
      Pages 19-19
    2. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 21-60
    3. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 61-88
    4. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 89-114
    5. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 115-144
    6. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 145-174
    7. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 175-194
    8. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 195-226
    9. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 227-252
    10. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 253-275
    11. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 277-297
    12. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 299-309
  4. Applications

    1. Front Matter
      Pages 311-311
    2. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 313-338
    3. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 339-361
    4. Jaroslav Nešetřil, Patrice Ossona de Mendez
      Pages 363-379

About this book

Introduction

This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants.

This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms.

Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris.

This book is related to the material presented by the first author at  ICM 2010.

Keywords

combinatorial algorithm graph decomposition graph minor sparse graphs structural graph theory

Authors and affiliations

  • Jaroslav Nešetřil
    • 1
  • Patrice Ossona de Mendez
    • 2
  1. 1.Department of Applied MathematicsCharles University Department of Applied MathematicsPragueCzech Republic
  2. 2.Mathématique Sociales (UMR 8557)CNRS Centre d'Analyse et deParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-27875-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-27874-7
  • Online ISBN 978-3-642-27875-4
  • Series Print ISSN 0937-5511
  • About this book