منابع مشابه
Cop-Win Graphs and Robber-Win Graphs
Let G be a finite connected graph of order at least two. Two players (a cop and a robber) are allowed to play a game on G according to the following rule: The cop chooses a vertex to stay then the robber chooses a vertex afterwards. After that they move alternately along edges of G, where the robber may opt to stay put when his turn to move comes. The cop wins if he succeeds in putting himself ...
متن کاملOn cop-win graphs
Following a question of Anstee and Farber we investigate the possibility that all bridged graphs are cop-win. We show that in7nite chordal graphs, even of diameter two, need not be cop-win and point to some interesting questions, some of which we answer. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملBridged Graphs Are Cop-Win Graphs: An Algorithmic Proof
A graph is bridged if it contains no isometric cycles of length greater than three. Anstee and Farber established that bridged graphs are cop-win graphs. According to Nowakowski and Winkler and Quilliot, a graph is a cop-win graph if and only if its vertices admit a linear ordering v1 , v2 , ..., vn such that every vertex vi , i>1, is dominated by some neighbour vj , j<i, i.e., every vertex vk ...
متن کاملEdge contraction and cop-win critical graphs
The problem is to determine the number of ‘cops’ needed to capture a ‘robber’ where the game is played with perfect information, the different sides moving alternately. The cops capture the robber when one of them occupies the same vertex as the robber at any time in the game. A copwin graph is one in which one cop can always capture the robber. A graph is cop-win edge-critical with respect to ...
متن کاملCop-Win Graphs with Maximal Capture-Time
Cop and robber is a two-player vertex-pursuit combinatorial game where the players stand on the vertices of a graph and alternate in moving to adjacent vertices. The cop wins when he captures the robber, robber’s goal is to avoid capture. The game has been studied in various modifications, many of which have an interesting relationship to certain well-known graph parameters, such as treewidth. ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.11.016