Almost all k-cop-win graphs contain a dominating set of cardinality k

被引：0
|
作者：
Pralat, Pawel [1 ]
机构：
[1] Ryerson Univ, Dept Math, Toronto, ON M5B 2K3, Canada
来源：
DISCRETE MATHEMATICS | 2015年 / 338卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
k-cop-win graph; Random graphs; ROBBERS;
D O I：
10.1016/j.disc.2014.08.023
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 is an element of 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(n2/2-(1/2-log2(1-2-k))n). (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：47 / 52
页数：6
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