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

页码：716 / 723

页数：8

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