Bounds on the k-restricted arc connectivity of some bipartite tournaments

For k ≥ 2, a strongly connected digraph D is called λk′-connected if it contains a set of arcs W such that D−W contains at least k non-trivial strong components. The k-restricted arc connectivity of a digraph D was defined by Volkmann as λk′(D)=min{|W|:Wisak-restrictedarc-cut}. In this paper we boun...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 331; pp. 54 - 60
Main Authors: Balbuena, C., González-Moreno, D., Olsen, M.
Format: Journal Article Publication
Language:English
Published: Elsevier Inc 15.08.2018
Subjects:
65 Numerical analysis
65Y Computer aspects of numerical algorithms
Anàlisi numèrica
Bipartite
Classificació AMS
Digraphs
Matemàtiques i estadística
Numerical analysis
Projective plane
Tournament
Àrees temàtiques de la UPC
Bipartite
Tournament
Projective plane
Digraphs
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:For k ≥ 2, a strongly connected digraph D is called λk′-connected if it contains a set of arcs W such that D−W contains at least k non-trivial strong components. The k-restricted arc connectivity of a digraph D was defined by Volkmann as λk′(D)=min{|W|:Wisak-restrictedarc-cut}. In this paper we bound λk′(T) for a family of bipartite tournaments T called projective bipartite tournaments. We also introduce a family of “good” bipartite oriented digraphs. For a good bipartite tournament T we prove that if the minimum degree of T is at least 1.5k−1 then k(k−1)≤λk′(T)≤k(N−2k−2), where N is the order of the tournament. As a consequence, we derive better bounds for circulant bipartite tournaments.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.02.038