Induced packing of odd cycles in planar graphs

Authors:
Petr A. Golovach;Marcin Kamiski;Danië/l Paulusma;Dimitrios M. Thilikos
Affiliations:
School of Engineering and Computing Sciences, University of Durham, United Kingdom;FNRS/ Dé/partement dInformatique, Université/ Libre de Bruxelles, Belgium;School of Engineering and Computing Sciences, University of Durham, United Kingdom;Departement of Mathematics, National and Kapodistrian University of Athens, Greece
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

An induced packing of odd cycles in a graph is a packing such that there is no edge in the graph between any two odd cycles in the packing. We prove that an induced packing of k odd cycles in an n-vertex graph can be found (if it exists) in time 2^O^(^k^^^3^^^/^^^2^)@?n^2^+^@e (for any constant @e0) when the input graph is planar. We also show that deciding if a graph has an induced packing of two odd induced cycles is NP-complete.