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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| Vydáno v: | Applied mathematics and computation Ročník 331; s. 54 - 60 |
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15.08.2018
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | 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. |
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| AbstractList | 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. For k¿=¿2, a strongly connected digraph D is called -connected if it contains a set of arcs W such that contains at least k non-trivial strong components. The k-restricted arc connectivity of a digraph D was defined by Volkmann as . In this paper we bound 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 then where N is the order of the tournament. As a consequence, we derive better bounds for circulant bipartite tournaments. Peer Reviewed |
| Author | Olsen, M. Balbuena, C. González-Moreno, D. |
| Author_xml | – sequence: 1 givenname: C. orcidid: 0000-0003-4190-4287 surname: Balbuena fullname: Balbuena, C. email: m.camino.balbuena@upc.edu organization: Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Unidad Cuajimalpa, México D.F., México – sequence: 2 givenname: D. surname: González-Moreno fullname: González-Moreno, D. email: dgonzalez@correo.cua.uam.mx organization: Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Unidad Cuajimalpa, México D.F., México – sequence: 3 givenname: M. surname: Olsen fullname: Olsen, M. email: olsen@correo.cua.uam.mx organization: Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Unidad Cuajimalpa, México D.F., México |
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| Snippet | 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... For k¿=¿2, a strongly connected digraph D is called -connected if it contains a set of arcs W such that contains at least k non-trivial strong components. The... |
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| SubjectTerms | 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 |
| Title | Bounds on the k-restricted arc connectivity of some bipartite tournaments |
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