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Thirty Essays on Geometric Graph Theory

  • Geometric graph theory is a fairly new discipline, which serves as a theoretical basis for information visualization and graph drawing

  • By mixing combinatorial, geometric, and topological methods, geometric graph theory has created an impressive toolbox for mathematicians and computer scientists

  • Contains 30 original survey and research papers on important recent developments in geometric graph theory

  • With contributions by leading researchers in this field

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Table of contents (32 chapters)

  1. Front Matter

    Pages i-xiii
  2. Introduction

    • János Pach
    Pages 1-4
  3. The Rectilinear Crossing Number of K n : Closing in (or Are We?)

    • Bernardo M. Ábrego, Silvia Fernández-Merchant, Gelasio Salazar
    Pages 5-18
  4. Blocking Colored Point Sets

    • Greg Aloupis, Brad Ballinger, Sébastien Collette, Stefan Langerman, Attila Pór, David R. Wood
    Pages 31-48
  5. Constrained Tri-Connected Planar Straight Line Graphs

    • Marwan Al-Jubeh, Gill Barequet, Mashhood Ishaque, Diane L. Souvaine, Csaba D. Tóth, Andrew Winslow
    Pages 49-70
  6. Topological Hypergraphs

    • Sarit Buzaglo, Rom Pinchasi, Günter Rote
    Pages 71-81
  7. On Edge-Disjoint Empty Triangles of Point Sets

    • Javier Cano, Luis F. Barba, Toshinori Sakai, Jorge Urrutia
    Pages 83-100
  8. Universal Sets for Straight-Line Embeddings of Bicolored Graphs

    • Josef Cibulka, Jan Kynčl, Viola Mészáros, Rudolf Stolař, Pavel Valtr
    Pages 101-119
  9. The Crossing-Angle Resolution in Graph Drawing

    • Walter Didimo, Giuseppe Liotta
    Pages 167-184
  10. Mover Problems

    • Adrian Dumitrescu
    Pages 185-211
  11. Convex Obstacle Numbers of Outerplanar Graphs and Bipartite Permutation Graphs

    • Radoslav Fulek, Noushin Saeedi, Deniz Sarıöz
    Pages 249-261
  12. Hanani–Tutte, Monotone Drawings, and Level-Planarity

    • Radoslav Fulek, Michael J. Pelsmajer, Marcus Schaefer, Daniel Štefankovič
    Pages 263-287
  13. On Disjoint Crossing Families in Geometric Graphs

    • Radoslav Fulek, Andrew Suk
    Pages 289-302
  14. Counting Plane Graphs: Flippability and Its Applications

    • Michael Hoffmann, André Schulz, Micha Sharir, Adam Sheffer, Csaba D. Tóth, Emo Welzl
    Pages 303-325
  15. Plane Geometric Graph Augmentation: A Generic Perspective

    • Ferran Hurtado, Csaba D. Tóth
    Pages 327-354
  16. Discrete Geometry on Red and Blue Points in the Plane Lattice

    • Mikio Kano, Kazuhiro Suzuki
    Pages 355-369
  17. Ramsey-Type Problems for Geometric Graphs

    • Gyula Károlyi
    Pages 371-382

About this book

In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions.

This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory.  The contributions were thoroughly reviewed and written by excellent researchers in this field.

Editors and Affiliations

  • Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    János Pach

  • École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    János Pach

About the editor

János Pach is a mathematician and computer scientist with academic and research positions in the following institutions: École Polytechnique Fédérale de Lausanne,  Alfréd Rényi Institute of Mathematics at Hungarian Academy of Sciences, and Courant Institute of Mathematics at NYU.

Bibliographic Information

  • Book Title: Thirty Essays on Geometric Graph Theory

  • Editors: János Pach

  • DOI: https://doi.org/10.1007/978-1-4614-0110-0

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media New York 2013

  • Hardcover ISBN: 978-1-4614-0109-4Published: 14 December 2012

  • Softcover ISBN: 978-1-4939-0253-8Published: 28 January 2015

  • eBook ISBN: 978-1-4614-0110-0Published: 15 December 2012

  • Edition Number: 1

  • Number of Pages: XIV, 610

  • Topics: Discrete Mathematics, Geometry, Combinatorics

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access