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A Fixed-Parameter Algorithm for the Max-Cut Problem on Embedded 1-Planar Graphs

  • Christine DahnEmail author
  • Nils M. Kriege
  • Petra Mutzel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)

Abstract

We propose a fixed-parameter tractable algorithm for the Max-Cut problem on embedded 1-planar graphs parameterized by the crossing number k of the given embedding. A graph is called 1-planar if it can be drawn in the plane with at most one crossing per edge. Our algorithm recursively reduces a 1-planar graph to at most \(3^k\) planar graphs, using edge removal and node contraction. The Max-Cut problem is then solved on the planar graphs using established polynomial-time algorithms. We show that a maximum cut in the given 1-planar graph can be derived from the solutions for the planar graphs. Our algorithm computes a maximum cut in an embedded 1-planar graph with n nodes and k edge crossings in time \(\mathcal {O}(3^k \cdot n^{3/2} \log n)\).

Keywords

Maximum cut Fixed-parameter tractable 1-planar graphs 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceTU Dortmund UniversityDortmundGermany

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