The fast robber on interval and chordal graphs
نویسندگان
چکیده
منابع مشابه
Cops and Robber Game with a Fast Robber on Interval, Chordal, and Planar Graphs
We consider a variant of the Cops and Robber game, introduced by Fomin, Golovach, Kratochv́ıl, in which the robber has unbounded speed, i.e. can take any path from her vertex in her turn, but she is not allowed to pass through a vertex occupied by a cop. We study this game on interval graphs, chordal graphs, planar graphs, and hypercube graphs. Let c∞(G) denote the number of cops needed to captu...
متن کاملCatching a Fast Robber on Interval Graphs
We analyse the Cops and ∞-fast Robber game on the class of interval graphs and prove it to be polynomially decidable on such graphs. This solves an open problem posed in paper “Pursuing a fast robber on a graph” by Fomin et al. [4] The game is known to be already NP-hard on chordal graphs and split-graphs. The game is played by two players, one controlling k cops, the other a robber. The player...
متن کاملChasing a Fast Robber on Planar Graphs and Random Graphs
We consider a variant of the Cops and Robber game, in which the robber has unbounded speed, i.e., 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 treewidth of G. We show that if G is planar then c∞(G) = Θ(tw(G))...
متن کاملChordal graphs, interval graphs, and wqo
Let ! be the induced-minor relation. It is shown that, for every t, all chordal graphs of clique number at most t are well-quasi-ordered by !. On the other hand, if the bound on clique number is dropped, even the class of interval graphs is not well-quasi-ordered by !. c © 1998 John Wiley & Sons, Inc. J Graph Theory 28: 105–114, 1998
متن کاملFast Robber in Planar Graphs
In the cops and robber game, two players play alternately by moving their tokens along the edges of a graph. The first one plays with the cops and the second one with one robber. The cops aim at capturing the robber, while the robber tries to infinitely evade the cops. The main problem consists in minimizing the number of cops used to capture the robber in a graph. This minimum number is called...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.07.029