What Makes Equitable Connected Partition Easy

We study the Equitable Connected Partition problem, which is the problem of partitioning a graph into a given number of partitions, such that each partition induces a connected subgraph, and the partitions differ in size by at most one. We examine the problem from the parameterized complexity perspective with respect to the number of partitions, the treewidth, the pathwidth, the size of a minimum feedback vertex set, the size of a minimum vertex cover, 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 parameters (even combined), whereas it becomes fixed-parameter tractable when parameterized by the last two parameters. The hardness result remains true even for planar graphs. We also show that the problem is in XP when parameterized by the treewidth (and hence any other mentioned structural parameter). Furthermore, we show that the closely related problem, Equitable Coloring, is FPT wh...

• Type: Conference
• Year: 2009
• Where: IWPEC
• Authors: Rosa Enciso, Michael R. Fellows, Jiong Guo, Iyad A. Kanj, Frances A. Rosamond, Ondrej Suchý
• Keywords: Applied Computing, Connected Partition Problem, IWPEC 2009, Maximum Number, Parameterized Complexity Perspective