Induced Packing of Odd Cycles in a Planar Graph

  • Authors:

  • Petr A. Golovach;Marcin Kamiński;Daniël Paulusma;Dimitrios M. Thilikos

  • Affiliations:

  • Department of Computer Science, University of Bergen,;Department of Computer Science, Université Libre de Bruxelles,;Department of Computer Science, University of Durham,;Department of Mathematics, National and Kapodistrian University of Athens,

  • Venue:
  • ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
  • Year:
  • 2009

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Abstract

An induced packing of odd cycles in a graph is a packing such that there is no edge in a graph between any two odd cycles in the packing. We prove that the problem is solvable in time $2^{{\cal O}(k^{3/2})} \cdot n^3 \log n$ when the input graph is planar. We also show that deciding if a graph has an induced packing of two odd cycles is NP-complete.