Graphs and Combinatorics

, Volume 14, Issue 1, pp 59–73

The Thickness of Graphs: A Survey

  • Petra Mutzel
  • Thomas Odenthal
  • Mark Scharbrodt

DOI: 10.1007/PL00007219

Cite this article as:
Mutzel, P., Odenthal, T. & Scharbrodt, M. Graphs Comb (1998) 14: 59. doi:10.1007/PL00007219


 We give a state-of-the-art survey of the thickness of a graph from both a theoretical and a practical point of view. After summarizing the relevant results concerning this topological invariant of a graph, we deal with practical computation of the thickness. We present some modifications of a basic heuristic and investigate their usefulness for evaluating the thickness and determining a decomposition of a graph in planar subgraphs.

Key words: Thicknessmaximum planar subgraphbranch and cut

Copyright information

© Springer-Verlag Tokyo 1998

Authors and Affiliations

  • Petra Mutzel
    • 1
  • Thomas Odenthal
    • 2
  • Mark Scharbrodt
    • 3
  1. 1. Max-Planck-Institut fu¨r Informatik, Im Stadtwald, D-66123 Saarbru¨cken, GermanyDE
  2. 2. IEOR-Department, Columbia University, 331 Mudd, New York, NY 10027, USAUS
  3. 3. Lehrstuhl fu¨r Brauereianlagen und Lebensmittel-Verpackungstechnik, TU-Mu¨nchen – Weihenstephan, D-85350 Freising, GermanyDE