@article{e5acd6419d9944bdbf56b47fc24d3119,

title = "Chasing a fast robber on planar graphs and random graphs",

abstract = "We consider a variant of the Cops and Robber game, in which the robber has unbounded speed, that is, can take any path from her vertex in her turn, but she is not allowed to pass through a vertex occupied by a cop. Let c∞(G) denote the number of cops needed to capture the robber in a graph G in this variant, and let tw(G) denote the tree-width of G. We show that if G is planar then c∞(G) = Θ(tw(G)), and there is a polynomial-time constant-factor approximation algorithm for computing c∞(G).We also determine, up to constant factors, the value of c∞(G) of the Erdo″s-R{\'e}nyi random graph G = G(n, p) for all admissible values of p, and show that when the average degree is ω(1), c∞(G) is typically asymptotic to the domination number.",

keywords = "Cops and robber game, Domination number, Fast robber, Planar graphs, Random graphs, Treewidth",

author = "Noga Alon and Abbas Mehrabian",

note = "Publisher Copyright: {\textcopyright} 2014 Wiley Periodicals, Inc.",

year = "2015",

month = jan,

day = "1",

doi = "10.1002/jgt.21791",

language = "אנגלית",

volume = "78",

pages = "81--96",

journal = "Journal of Graph Theory",

issn = "0364-9024",

publisher = "Wiley-Liss Inc.",

number = "2",

}