Counting orientations of graphs with no strongly connected tournaments

Detalhes bibliográficos
Autor(a) principal: Botler, Fábio Happ
Data de Publicação: 2021
Outros Autores: Hoppen, Carlos, Mota, Guilherme Oliveira
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/246962
Resumo: Let Sk(n) be the maximum number of orientations of an n-vertex graph G in which no copy of Kk is strongly connected. For all integers n, k ≥ 4 where n ≥ 5 or k ≥ 5, we prove that Sk(n) = 2tk - 1(n), where tk-1(n) is the number of edges of the n-vertex (k - 1)-partite Turán graph Tk-1(n). Moreover, we prove that Tk-1(n) is the only graph having 2tk-1(n) orientations with no strongly connected copies of Kk.
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spelling Botler, Fábio HappHoppen, CarlosMota, Guilherme Oliveira2022-08-16T04:47:07Z20211877-0509http://hdl.handle.net/10183/246962001136295Let Sk(n) be the maximum number of orientations of an n-vertex graph G in which no copy of Kk is strongly connected. For all integers n, k ≥ 4 where n ≥ 5 or k ≥ 5, we prove that Sk(n) = 2tk - 1(n), where tk-1(n) is the number of edges of the n-vertex (k - 1)-partite Turán graph Tk-1(n). Moreover, we prove that Tk-1(n) is the only graph having 2tk-1(n) orientations with no strongly connected copies of Kk.application/pdfengProcedia Computer Science. Amsterdam. Vol. 195 (2021), p. 385 - 393GrafosOrientaçãoOrientationsTournamentsComplete graphsCounting orientations of graphs with no strongly connected tournamentsEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001136295.pdf.txt001136295.pdf.txtExtracted Texttext/plain34518http://www.lume.ufrgs.br/bitstream/10183/246962/2/001136295.pdf.txte186cb199ae1f7ccb550660e9fa395aeMD52ORIGINAL001136295.pdfTexto completo (inglês)application/pdf387809http://www.lume.ufrgs.br/bitstream/10183/246962/1/001136295.pdfad712be198a1f3ea7cb642b3bef460b9MD5110183/2469622022-08-17 04:48:52.823486oai:www.lume.ufrgs.br:10183/246962Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2022-08-17T07:48:52Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Counting orientations of graphs with no strongly connected tournaments
title Counting orientations of graphs with no strongly connected tournaments
spellingShingle Counting orientations of graphs with no strongly connected tournaments
Botler, Fábio Happ
Grafos
Orientação
Orientations
Tournaments
Complete graphs
title_short Counting orientations of graphs with no strongly connected tournaments
title_full Counting orientations of graphs with no strongly connected tournaments
title_fullStr Counting orientations of graphs with no strongly connected tournaments
title_full_unstemmed Counting orientations of graphs with no strongly connected tournaments
title_sort Counting orientations of graphs with no strongly connected tournaments
author Botler, Fábio Happ
author_facet Botler, Fábio Happ
Hoppen, Carlos
Mota, Guilherme Oliveira
author_role author
author2 Hoppen, Carlos
Mota, Guilherme Oliveira
author2_role author
author
dc.contributor.author.fl_str_mv Botler, Fábio Happ
Hoppen, Carlos
Mota, Guilherme Oliveira
dc.subject.por.fl_str_mv Grafos
Orientação
topic Grafos
Orientação
Orientations
Tournaments
Complete graphs
dc.subject.eng.fl_str_mv Orientations
Tournaments
Complete graphs
description Let Sk(n) be the maximum number of orientations of an n-vertex graph G in which no copy of Kk is strongly connected. For all integers n, k ≥ 4 where n ≥ 5 or k ≥ 5, we prove that Sk(n) = 2tk - 1(n), where tk-1(n) is the number of edges of the n-vertex (k - 1)-partite Turán graph Tk-1(n). Moreover, we prove that Tk-1(n) is the only graph having 2tk-1(n) orientations with no strongly connected copies of Kk.
publishDate 2021
dc.date.issued.fl_str_mv 2021
dc.date.accessioned.fl_str_mv 2022-08-16T04:47:07Z
dc.type.driver.fl_str_mv Estrangeiro
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dc.identifier.issn.pt_BR.fl_str_mv 1877-0509
dc.identifier.nrb.pt_BR.fl_str_mv 001136295
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dc.relation.ispartof.pt_BR.fl_str_mv Procedia Computer Science. Amsterdam. Vol. 195 (2021), p. 385 - 393
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eu_rights_str_mv openAccess
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reponame_str Repositório Institucional da UFRGS
collection Repositório Institucional da UFRGS
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