Estudo de complexidade de jogos de coloração

• Autor(a) principal: Pessoa, Victor Lage
• Data de Publicação: 2019
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/43286
• topic: Coloração de Grafos; Número Cromático Lúdico; Número de Grundy Lúdico

We answer in this dissertation a question that remained unanswered for the last 28 years: the complexity of Bodlaender’s graph coloring game. The coloring game in a simple graph G is played by two players: Alice and Bob, each has the same set of colors C having k distinct colors. In alternating turns, each chooses a single not yet colored vertex from G and a color from C used to color such vertex in a way that adjacent vertices have distinct colors. Alice wins the game when all vertices from G are properly colored and Bob wins if at any moment there is a vertex which cannot be colored by any of the k colors from C . We also studied the complexity of a variant of the game called the greed coloring game and obtained the game Grundy number for graphs of the P4 -sparse class in such game.