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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.