Almost all cop-win graphs contain a universal vertex
نویسندگان
چکیده
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.
منابع مشابه
Almost 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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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 312 شماره
صفحات -
تاریخ انتشار 2012