An Algorithm for Finding Large Induced Planar Subgraphs

  • Keith Edwards
  • Graham Farr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)

Abstract

This paper presents an efficient algorithm that finds an induced planar subgraph of at least 3n/(d + 1) vertices in a graph of n vertices and maximum degree d. This bound is sharp for d = 3, in the sense that if ɛ > 3/4 then there are graphs of maximum degree 3 with no induced planar subgraph of at least ɛn vertices. Our performance ratios appear to be the best known for small d. For example, when d = 3, our performance ratio of at least 3/4 compares with the ratio 1/2 obtained by Halldórsson and Lau. Our algorithm builds up an induced planar subgraph by iteratively adding a new vertex to it, or swapping a vertex in it with one outside it, in such a way that the procedure is guaranteed to stop, and so as to preserve certain properties that allow its performance to be analysed. This work is related to the authors’ work on fragmentability of graphs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Keith Edwards
    • 1
  • Graham Farr
    • 2
  1. 1.Department of Applied ComputingUniversity of DundeeDundeeUK
  2. 2.School of Computer Science and Software EngineeringMonash University (Clayton Campus)ClaytonAustralia

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