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The Effect of Planarization on Width

  • David EppsteinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10692)

Abstract

We study the effects of planarization (the construction of a planar diagram D from a non-planar graph G by replacing each crossing by a new vertex) on graph width parameters. We show that for treewidth, pathwidth, branchwidth, clique-width, and tree-depth there exists a family of n-vertex graphs with bounded parameter value, all of whose planarizations have parameter value \(\varOmega (n)\). However, for bandwidth, cutwidth, and carving width, every graph with bounded parameter value has a planarization of linear size whose parameter value remains bounded. The same is true for the treewidth, pathwidth, and branchwidth of graphs of bounded degree.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaIrvineUSA

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