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Author Fomin, F.V.; Golovach, P.A.; Kratochvil, J.; Nisse, N.; Suchan, K. pdf  doi
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  Title Pursuing a fast robber on a graph Type Journal Article
  Year 2010 Publication Theoretical Computer Science Abbreviated Journal Theor. Comput. Sci.  
  Volume 411 Issue 7-9 Pages 1167-1181  
  Keywords Pursuit-evasion game on graphs; Cops and Robbers; Complexity; Parameterized complexity; Cliquewidth; Planar graph  
  Abstract The Cops and Robbers game as originally defined independently by Quilliot and by Nowakowski and Winkler in the 1980s has been Much Studied, but very few results pertain to the algorithmic and complexity aspects of it. In this paper we prove that computing the minimum number of cops that are guaranteed to catch a robber on a given graph is NP-hard and that the parameterized version of the problem is W[2]-hard; the proof extends to the case where the robber moves s time faster than the cops. We show that on split graphs, the problem is polynomially solvable if s = 1 but is NP-hard if s = 2. We further prove that on graphs of bounded cliquewidth the problem is polynomially solvable for s <= 2. Finally, we show that for planar graphs the minimum number of cops is unbounded if the robber is faster than the cops. (C) 2009 Elsevier B.V. All rights reserved.  
  Address [Fomin, Fedor V.; Golovach, Petr A.] Univ Bergen, Dept Informat, N-5020 Bergen, Norway, Email: petr.golovach@durham.ac.uk  
  Corporate Author Thesis  
  Publisher Elsevier Science Bv Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0304-3975 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000274886700020 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 83  
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Author Golovach, P.A.; Heggernes, P.; Lima, P.T.; Montealegre, P. doi  openurl
  Title Finding connected secluded subgraphs Type Journal Article
  Year 2020 Publication Journal Of Computer And System Sciences Abbreviated Journal J. Comput. Syst. Sci.  
  Volume 113 Issue Pages 101-124  
  Keywords Secluded subgraph; Parameterized complexity; Forbidden subgraphs  
  Abstract Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. However, 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 Pi-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 Pi, even when parameterized by k + t. We show that the situation changes when we are looking for a connected induced subgraph satisfying Pi. In particular, we show that the CONNECTED SECLUDED Pi-SUBGRAPH problem is FPT when parameterized by just t for many important graph properties Pi. (C) 2020 Elsevier Inc. All rights reserved.  
  Address [Golovach, Petr A.; Heggernes, Pinar; Lima, Paloma T.] Univ Bergen, Dept Informat, N-5020 Bergen, Norway, Email: petr.golovach@uib.no;  
  Corporate Author Thesis  
  Publisher Academic Press Inc Elsevier Science Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0022-0000 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000539435200006 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 1191  
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