Almost all k-cop-win graphs contain a dominating set of cardinality k
نویسنده
چکیده
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 /2−(1/2−log2(1−2 ))n.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 338 شماره
صفحات -
تاریخ انتشار 2015