Finding k disjoint triangles in an arbitrary graph

  • Authors:

  • Mike Fellows;Pinar Heggernes;Frances Rosamond;Christian Sloper;Jan Arne Telle

  • Affiliations:

  • School of Electrical Engineering and Computer Science, University of Newcastle, Australia;Department of Informatics, University of Bergen, Norway;School of Electrical Engineering and Computer Science, University of Newcastle, Australia;Department of Informatics, University of Bergen, Norway;Department of Informatics, University of Bergen, Norway

  • Venue:
  • WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
  • Year:
  • 2004

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Abstract

We consider the NP-complete problem of deciding whether an input graph on n vertices has k vertex-disjoint copies of a fixed graph H. For H=K3 (the triangle) we give an O(22klog k+1.869kn2) algorithm, and for general H an O(2k|H|logk+2k|H|log |H|n|H|) algorithm. We introduce a preprocessing (kernelization) technique based on crown decompositions of an auxiliary graph. For H=K3 this leads to a preprocessing algorithm that reduces an arbitrary input graph of the problem to a graph on O(k3) vertices in polynomial time.