Feedback numbers of de Bruijn digraphs

被引：9
|
作者：
Xu, Xirong [1 ,2 ]
Cao, Yongchang [1 ]
Xu, Jun-Ming [1 ]
Wu, Yezhou [1 ]
机构：
[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China
[2] Dalian Univ Technol, Dept Comp Sci, Dalian 116024, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 02期
关键词：
Feedback vertex set; Feedback number; de Bruijn digraphs; Cycles; Acyclic subgraph; VERTEX SET PROBLEM;
D O I：
10.1016/j.camwa.2009.10.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A subset of vertices of a graph G is called a feedback vertex set of G if its removal results in an acyclic subgraph. Let f (d, n) denote the minimum cardinality over all feedback vertex sets of the de Bruijn digraph B(d, n). This paper proves that for any integers d >= 2 and n >= 2 f(d, n) = {1/n Sigma(i|n) di phi (n/i) for 2 <= n <= 4; d(n)/n + o(nd(n-4)) for n >= 5, where i I n means i divides n, and co(i) is the Euler totient function. (C) 2009 Published by Elsevier Ltd
引用
收藏
页码：716 / 723
页数：8
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