On self duality of pathwidth in polyhedral graph embeddings

  • Authors:

  • Fedor V. Fomin;Dimitrios M. Thilikos

  • Affiliations:

  • Department of Informatics, University of Bergen, N-5020 Bergen, Norway;Department of Mathematics, National and Capodistrian University of Athens, Panepistimioupolis, GR-15784, Athens, Greece

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2007

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Abstract

Let G be a 3-connected planar graph and G* be its dual. We show that the pathwidth of G* is at most 6 times the pathwidth of G. We prove this result by relating the pathwidth of a graph with the cut-width of its medial graph and we extend it to bounded genus embeddings. We also show that there exist 3-connected planar graphs such that the pathwidth of such a graph is at least 1.5 times the pathwidth of its dual. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 42–54, 2007