Almost all cop-win graphs contain a universal vertex
نویسندگان
چکیده
منابع مشابه
Almost all cop-win graphs contain a universal vertex
We consider cop-win graphs in the binomial random graph G(n, 1/2). We prove that almost all cop-win graphs contain a universal vertex. From this result, we derive that the asymptotic number of labelled cop-win graphs of order n is equal to (1 + o(1))n2 2/2−3n/2+1.
متن کاملAlmost All Cop-win Graphs Have a Universal Vertex
Cops and Robbers is a vertex-pursuit game played on graphs which has received much recent attention. Graphs where one cop has a winning strategy, so-called cop-win graphs, were discovered in the early 1980’s by Nowakowski and Winkler and independently by Quilliot. Since their introduction, the structure of cop-win graphs has been relatively well-understood. Cop-win graphs possess a vertex elimi...
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We consider k-cop-win graphs in the binomial random graph G(n, 1/2). It is known that almost all cop-win graphs contain a universal vertex. We generalize this result and prove that for every k ∈ N, almost all k-cop-win graphs contain a dominating set of cardinality k. From this it follows that the asymptotic number of labelled k-cop-win graphs of order n is equal to (1+o(1))(1−2−k)−k ( n k ) 2 ...
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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.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.02.018