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Digraphs that have at most one walk of a given length with the same endpoints

Let [theta](n,k) be the set of digraphs of order n that have at most one walk of length k with the same endpoints. Let [theta](n,k) be the maximum number of arcs of a digraph in [theta](n,k). We prove that if n>=5 and k>=n-1 then [theta](n,k)=n(n-1)/2 and this maximum number is attained at D if and... Full description

Journal Title: Discrete Mathematics Jan 6, 2011, Vol.311(1), pp.70-79
Main Author: Huang, Zejun
Other Authors: Zhan, Xingzhi
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 0012-365X ; DOI: 10.1016/j.disc.2010.09.025
Link: http://search.proquest.com/docview/1671289367/
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title: Digraphs that have at most one walk of a given length with the same endpoints
format: Article
creator:
  • Huang, Zejun
  • Zhan, Xingzhi
subjects:
  • Mathematical Analysis
  • Discrete Mathematics (Ci)
ispartof: Discrete Mathematics, Jan 6, 2011, Vol.311(1), pp.70-79
description: Let [theta](n,k) be the set of digraphs of order n that have at most one walk of length k with the same endpoints. Let [theta](n,k) be the maximum number of arcs of a digraph in [theta](n,k). We prove that if n>=5 and k>=n-1 then [theta](n,k)=n(n-1)/2 and this maximum number is attained at D if and only if D is a transitive tournament. [theta](n,n-2) and [theta](n,n-3) are also determined.
language: eng
source:
identifier: ISSN: 0012-365X ; DOI: 10.1016/j.disc.2010.09.025
fulltext: fulltext
issn:
  • 0012365X
  • 0012-365X
url: Link


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descriptionLet [theta](n,k) be the set of digraphs of order n that have at most one walk of length k with the same endpoints. Let [theta](n,k) be the maximum number of arcs of a digraph in [theta](n,k). We prove that if n>=5 and k>=n-1 then [theta](n,k)=n(n-1)/2 and this maximum number is attained at D if and only if D is a transitive tournament. [theta](n,n-2) and [theta](n,n-3) are also determined.
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abstractLet [theta](n,k) be the set of digraphs of order n that have at most one walk of length k with the same endpoints. Let [theta](n,k) be the maximum number of arcs of a digraph in [theta](n,k). We prove that if n>=5 and k>=n-1 then [theta](n,k)=n(n-1)/2 and this maximum number is attained at D if and only if D is a transitive tournament. [theta](n,n-2) and [theta](n,n-3) are also determined.
doi10.1016/j.disc.2010.09.025
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date2011-01-06