Cutwidth: Obstructions and Algorithmic Aspects

Archontia C. Giannopoulou, Michał Pilipczuk, Jean Florent Raymond, Dimitrios M. Thilikos, Marcin Wrochna

Research output: Contribution to journalArticlepeer-review


Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As graphs of cutwidth at most k are closed under taking immersions, the results of Robertson and Seymour imply that there is a finite list of minimal immersion obstructions for admitting a cut layout of width at most k. We prove that every minimal immersion obstruction for cutwidth at most k has size at most 2O(k3logk). As an interesting algorithmic byproduct, we design a new fixed-parameter algorithm for computing the cutwidth of a graph that runs in time 2O(k2logk)·n, where k is the optimum width and n is the number of vertices. While being slower by a log k-factor in the exponent than the fastest known algorithm, given by Thilikos et al. (J Algorithms 56(1):1–24, 2005; J Algorithms 56(1):25–49, 2005), our algorithm has the advantage of being simpler and self-contained; arguably, it explains better the combinatorics of optimum-width layouts.

Original languageEnglish (US)
Pages (from-to)557-588
Number of pages32
Issue number2
StatePublished - Feb 15 2019


  • Cutwidth
  • Fixed-parameter tractability
  • Immersions
  • Obstructions

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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