Proper colouring Painter–Builder game

We consider the following two-player game, parametrised by positive integers and . The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on vertices. In each round Painter colours a vertex of her choice by one of the...

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Detalles Bibliográficos
Autores: Bednarska-Bzdega, Malgorzata, Krivelevich, Michael, Mészáros, Viola, Requile, Clement|||0000-0002-7689-7972
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/406460
Acceso en línea:https://hdl.handle.net/2117/406460
https://dx.doi.org/10.1016/j.disc.2017.11.008
Access Level:acceso abierto
Palabra clave:Combinatorial games
Graph colouring
Classificació AMS::60 Probability theory and stochastic processes
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling Proper colouring Painter–Builder gameBednarska-Bzdega, MalgorzataKrivelevich, MichaelMészáros, ViolaRequile, Clement|||0000-0002-7689-7972Combinatorial gamesGraph colouringClassificació AMS::60 Probability theory and stochastic processesÀrees temàtiques de la UPC::Matemàtiques i estadísticaWe consider the following two-player game, parametrised by positive integers and . The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on vertices. In each round Painter colours a vertex of her choice by one of the colours and Builder adds an edge between two previously unconnected vertices. Both players must adhere to the restriction that the game graph is properly -coloured. The game ends if either all vertices have been coloured, or Painter has no legal move. In the former case, Painter wins the game; in the latter one, Builder is the winner. We prove that the minimal number of colours allowing Painter’s win is of logarithmic order in the number of vertices . Biased versions of the game are also considered.Peer Reviewed20182018-03-0120242024-04-12journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/406460https://dx.doi.org/10.1016/j.disc.2017.11.008reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4064602026-05-27T15:37:01Z
dc.title.none.fl_str_mv Proper colouring Painter–Builder game
title Proper colouring Painter–Builder game
spellingShingle Proper colouring Painter–Builder game
Bednarska-Bzdega, Malgorzata
Combinatorial games
Graph colouring
Classificació AMS::60 Probability theory and stochastic processes
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Proper colouring Painter–Builder game
title_full Proper colouring Painter–Builder game
title_fullStr Proper colouring Painter–Builder game
title_full_unstemmed Proper colouring Painter–Builder game
title_sort Proper colouring Painter–Builder game
dc.creator.none.fl_str_mv Bednarska-Bzdega, Malgorzata
Krivelevich, Michael
Mészáros, Viola
Requile, Clement|||0000-0002-7689-7972
author Bednarska-Bzdega, Malgorzata
author_facet Bednarska-Bzdega, Malgorzata
Krivelevich, Michael
Mészáros, Viola
Requile, Clement|||0000-0002-7689-7972
author_role author
author2 Krivelevich, Michael
Mészáros, Viola
Requile, Clement|||0000-0002-7689-7972
author2_role author
author
author
dc.subject.none.fl_str_mv Combinatorial games
Graph colouring
Classificació AMS::60 Probability theory and stochastic processes
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Combinatorial games
Graph colouring
Classificació AMS::60 Probability theory and stochastic processes
Àrees temàtiques de la UPC::Matemàtiques i estadística
description We consider the following two-player game, parametrised by positive integers and . The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on vertices. In each round Painter colours a vertex of her choice by one of the colours and Builder adds an edge between two previously unconnected vertices. Both players must adhere to the restriction that the game graph is properly -coloured. The game ends if either all vertices have been coloured, or Painter has no legal move. In the former case, Painter wins the game; in the latter one, Builder is the winner. We prove that the minimal number of colours allowing Painter’s win is of logarithmic order in the number of vertices . Biased versions of the game are also considered.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-03-01
2024
2024-04-12
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/406460
https://dx.doi.org/10.1016/j.disc.2017.11.008
url https://hdl.handle.net/2117/406460
https://dx.doi.org/10.1016/j.disc.2017.11.008
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
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