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Thread Graphs, Linear Rank-Width and Their Algorithmic Applications

  • Robert Ganian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Introduction

The introduction of tree-width by Robertson and Seymour [7] was a breakthrough in the design of graph algorithms. A lot of research since then has focused on obtaining a width measure which would be more general and still allowed efficient algorithms for a wide range of NP-hard problems on graphs of bounded width. To this end, Oum and Seymour have proposed rank-width, which allows the solution of many such hard problems on a less restricted graph classes (see e.g. [3,4]). But what about problems which are NP-hard even on graphs of bounded tree-width or even on trees? The parameter used most often for these exceptionally hard problems is path-width, however it is extremely restrictive – for example the graphs of path-width 1 are exactly paths.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Robert Ganian
    • 1
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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