- Title
- What makes equitable connected partition easy
- Creator
- Enciso, Rosa; Fellows, Michael R.; Guo, Jiong; Kanj, Iyad; Rosamond, Frances; Ondrej, Suchy
- Relation
- 4th International Workshop, Parameterized and Exact Computation (IWPEC 2009). Parameterized and Exact Computation 4th International Workshop, IWPEC 2009: Revised Selected Papers (Copenhagen, Denmark 10-11 September, 2009) p. 122-133
- Publisher Link
- http://dx.doi.org/10.1007/978-3-642-11269-0_10
- Publisher
- Springer Berlin
- Resource Type
- conference paper
- Date
- 2009
- Description
- 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.
- Subject
- equitable connected partition; equitable colouring; parameterized complexity; graphs
- Identifier
- uon:8862
- Identifier
- http://hdl.handle.net/1959.13/919426
- Identifier
- ISBN:9783642112683
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