An algorithm for finding large induced planar subgraphs

Keith Edwards, Graham Farr

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    8 Citations (Scopus)


    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 ? > 3/4 then there are graphs of maximum degree 3 with no induced planar subgraph of at least ?n 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 Halldorsson and Lau. Our algorithm builds up an induced planar subgraph by iteratively adding a newvertex 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.
    Original languageEnglish
    Title of host publicationGraph Drawing
    Subtitle of host publication9th International Symposium, GD 2001 Vienna, Austria, September 23–26, 2001 Revised Papers
    EditorsPetra Mutzel, Michael Junger, Sebastian Leipert
    Place of PublicationBerlin
    Number of pages9
    ISBN (Electronic)9783540458487
    ISBN (Print)9783540433095, 3540433090
    Publication statusPublished - 2002
    Event9th International Symposium on Graph Drawing - Vienna, Austria
    Duration: 23 Sept 200126 Sept 2001

    Publication series

    NameLecture notes in computer science
    ISSN (Print)0302-9743


    Conference9th International Symposium on Graph Drawing
    Abbreviated titleGD 2001


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