Finding connected secluded subgraphs

Petr A. Golovach, Pinar Heggernes, Paloma T. Lima, Pedro Montealegre

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. Such problems have given rise to breakthrough results and led to development of new techniques both within the traditional P vs NP dichotomy and within parameterized complexity. The Π-Subgraph problem asks whether an input graph contains an induced subgraph on at least k vertices satisfying graph property Π. For many applications, it is desirable that the found subgraph has as few connections to the rest of the graph as possible, which gives rise to the Secluded Π-Subgraph problem. Here, input k is the size of the desired subgraph, and input t is a limit on the number of neighbors this subgraph has in the rest of the graph. This problem has been studied from a parameterized perspective, and unfortunately it turns out to be W[1]-hard for many graph properties Π, even when parameterized by k + t. We show that the situation changes when we are looking for a connected induced subgraph satisfying Π. In particular, we show that the Connected Secluded Π-Subgraph problem is FPT when parameterized by just t for many important graph properties Π.

Original languageEnglish
Title of host publication12th International Symposium on Parameterized and Exact Computation, IPEC 2017
EditorsDaniel Lokshtanov, Naomi Nishimura
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770514
StatePublished - 1 Feb 2018
Externally publishedYes
Event12th International Symposium on Parameterized and Exact Computation, IPEC 2017 - Vienna, Austria
Duration: 6 Sep 20178 Sep 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference12th International Symposium on Parameterized and Exact Computation, IPEC 2017


  • Forbidden subgraphs
  • Parameterized complexity
  • Secluded subgraph


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