Title

What Makes Equitable Connected Partition Easy

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. © 2009 Springer-Verlag.

Publication Date

12-24-2009

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volume

5917 LNCS

Number of Pages

122-133

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/978-3-642-11269-0_10

Socpus ID

72249094214 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/72249094214

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