Parameterized Complexity of Connected Induced Subgraph Problems

  • Leizhen Cai
  • Junjie Ye
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)


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[1]-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[1]-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[1]-hard if H is K t with t ≥ 3 or K 1,s with s ≥ 2, and FPT otherwise.


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Leizhen Cai
    • 1
  • Junjie Ye
    • 1
  1. 1.Department of Computer Science and EngineeringThe Chinese University of Hong KongShatinHong Kong

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