Parameterized Complexity of Connected Induced Subgraph Problems
For a graph property Π, i.e., a collection Π of graphs, the Connected Induced Π-Subgraph problem asks whether a graph G contains k vertices V′ such that the induced subgraph G[V′] is connected and belongs to Π.
In this paper, we regard k as a parameter and study the parameterized complexity of Connected Induced Π-Subgraph for hereditary properties Π. We give an almost complete characterization in terms of whether Π includes all complete graphs, all stars, or all paths: FPT if Π includes all complete graphs and stars, or excludes some complete graphs, stars and paths; and W-hard otherwise (except the case that Π includes all complete graphs and paths but exclude some stars). For the remaining case, we show that it is W-hard if Π includes all complete graphs K t , excludes a star K 1,s but includes all trees of maximum degree less than s. Our results imply a complete characterization for Π being H-free graphs for a fixed graph H: W-hard if H is K t with t ≥ 3 or K 1,s with s ≥ 2, and FPT otherwise.
Unable to display preview. Download preview PDF.
- 7.Miller, M., Širán, J.: Moore graphs and beyond: a survey of the degree/diameter problem. Electronic Journal of Combinatorics 61, 1–63 (2005)Google Scholar
- 9.Naor, M., Schulman, L.J., Srinivasan, A.: Splitters and near-optimal derandomization. In: Proceedings of the 36th Annual Symposium of Foundations of Computer Science, pp. 182–191 (1995)Google Scholar