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...
| Autores: | , , , |
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| 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 |
| Sumario: | 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. |
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