What Makes Equitable Connected Partition Easy

  • Rosa Enciso
  • Michael R. Fellows
  • Jiong Guo
  • Iyad Kanj
  • Frances Rosamond
  • Ondřej Suchý
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5917)

Abstract

We study the Equitable Connected Partition problem: partitioning the vertices of a graph into a specified number of classes, such that each class of the partition induces a connected subgraph, so that the classes have cardinalities that differ by at most one. We examine the problem from the parameterized complexity perspective with respect to various (aggregate) parameterizations involving such secondary measurements as: (1) the number of partition classes, (2) the treewidth, (3) the pathwidth, (4) the minimum size of a feedback vertex set, (5) the minimum size of a vertex cover, (6) and the maximum number of leaves in a spanning tree of the graph. In particular, we show that the problem is W[1]-hard with respect to the first four combined, while it is fixed-parameter tractable with respect to each of the last two alone. The hardness result holds even for planar graphs. The problem is in XP when parameterized by treewidth, by standard dynamic programming techniques. Furthermore, we show that the closely related problem of Equitable Coloring (equitably partitioning the vertices into a specified number of independent sets) is FPT parameterized by the maximum number of leaves in a spanning tree of the graph.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rosa Enciso
    • 1
  • Michael R. Fellows
    • 2
  • Jiong Guo
    • 3
  • Iyad Kanj
    • 4
  • Frances Rosamond
    • 2
  • Ondřej Suchý
    • 5
  1. 1.School of Electrical Engineering and Computer ScienceUniversity of Central FloridaOrlando
  2. 2.University of NewcastleNewcastleAustralia
  3. 3.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany
  4. 4.School of ComputingDePaul UniversityChicago
  5. 5.Department of Applied Mathematics and Institute for Theoretical Computer ScienceCharles UniversityPrahaCzech Republic

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