On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs

Detalhes bibliográficos
Autor(a) principal: Cardoso, Domingos M.
Data de Publicação: 2017
Outros Autores: Dominic, Charles, Witkowski, Lukasz, Witkowski, Marcin
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/21068
Resumo: Cop Robber game is a two player game played on an undirected graph. In this game cops try to capture a robber moving on the vertices of the graph. The cop number of a graph is the least number of cops needed to guarantee that the robber will be caught. In this paper we presents results concerning games on $G^{\Xi}$, that is the graph obtained by connecting the corresponding vertices in $G$ and its complement $\overline{G}$. In particular we show that for planar graphs $c(G^{\Xi})\leq 3$. Furthermore we investigate the cop-edge critical graphs, i.e. graphs that for any edge $e$ in $G$ we have either $c(G-e)<c(G) \text{ or } c(G-e)>c(G)$. We show couple examples of cop-edge critical graphs having cop number equal to $3$.
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spelling On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphsCops and RobbersVertex-pursuit gamesCop Robber game is a two player game played on an undirected graph. In this game cops try to capture a robber moving on the vertices of the graph. The cop number of a graph is the least number of cops needed to guarantee that the robber will be caught. In this paper we presents results concerning games on $G^{\Xi}$, that is the graph obtained by connecting the corresponding vertices in $G$ and its complement $\overline{G}$. In particular we show that for planar graphs $c(G^{\Xi})\leq 3$. Furthermore we investigate the cop-edge critical graphs, i.e. graphs that for any edge $e$ in $G$ we have either $c(G-e)<c(G) \text{ or } c(G-e)>c(G)$. We show couple examples of cop-edge critical graphs having cop number equal to $3$.University of Calgary2017-12-11T12:20:18Z2017-12-01T00:00:00Z2017-12info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/21068eng1715-0868Cardoso, Domingos M.Dominic, CharlesWitkowski, LukaszWitkowski, Marcininfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:37:09Zoai:ria.ua.pt:10773/21068Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:53:57.318039Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs
title On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs
spellingShingle On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs
Cardoso, Domingos M.
Cops and Robbers
Vertex-pursuit games
title_short On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs
title_full On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs
title_fullStr On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs
title_full_unstemmed On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs
title_sort On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs
author Cardoso, Domingos M.
author_facet Cardoso, Domingos M.
Dominic, Charles
Witkowski, Lukasz
Witkowski, Marcin
author_role author
author2 Dominic, Charles
Witkowski, Lukasz
Witkowski, Marcin
author2_role author
author
author
dc.contributor.author.fl_str_mv Cardoso, Domingos M.
Dominic, Charles
Witkowski, Lukasz
Witkowski, Marcin
dc.subject.por.fl_str_mv Cops and Robbers
Vertex-pursuit games
topic Cops and Robbers
Vertex-pursuit games
description Cop Robber game is a two player game played on an undirected graph. In this game cops try to capture a robber moving on the vertices of the graph. The cop number of a graph is the least number of cops needed to guarantee that the robber will be caught. In this paper we presents results concerning games on $G^{\Xi}$, that is the graph obtained by connecting the corresponding vertices in $G$ and its complement $\overline{G}$. In particular we show that for planar graphs $c(G^{\Xi})\leq 3$. Furthermore we investigate the cop-edge critical graphs, i.e. graphs that for any edge $e$ in $G$ we have either $c(G-e)<c(G) \text{ or } c(G-e)>c(G)$. We show couple examples of cop-edge critical graphs having cop number equal to $3$.
publishDate 2017
dc.date.none.fl_str_mv 2017-12-11T12:20:18Z
2017-12-01T00:00:00Z
2017-12
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/21068
url http://hdl.handle.net/10773/21068
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1715-0868
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv University of Calgary
publisher.none.fl_str_mv University of Calgary
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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