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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
  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  
  Call Number UAI @ eduardo.moreno @ Serial 83  
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