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Optimization and Recognition for K5-minor Free Graphs in Linear Time

  • Bruce Reed
  • Zhentao Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4957)

Abstract

We present a linear time algorithm which determines whether an input graph contains K 5 as a minor and outputs a K 5-model if the input graph contains one. If the input graph has no K 5-minor then the algorithm constructs a tree decomposition such that each node of the tree corresponds to a planar graph or a graph with eight vertices. Such a decomposition can be used to obtain algorithms to solve various optimization problems in linear time. For example, we present a linear time algorithm for finding an \(O(\sqrt{n})\) seperator and a linear time algorithm for solving k-realisation on graphs without a K 5-minor. Our algorithm will also be used, in a separate paper, as a key subroutine in a nearly linear time algorithm to test for the existence of an H-minor for any fixed H.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Bruce Reed
    • 1
    • 2
  • Zhentao Li
    • 3
  1. 1.Canada Research Chair in Graph TheoryMcGill UniversityMontrealCanada
  2. 2.Project MascotteINRIACNRS, Sophia-AntipolisFrance
  3. 3.School of Computer ScienceMcGill UniversityMontrealCanada

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