Theory of Combinatorial Games in Graphs
Description
This book offers a comprehensive introduction to the field of combinatorial games, with a contemporary focus on games played on graphs. It provides a clear, structured tour of the major classes of combinatorial games (normal, misère, impartial, partizan, and positional), illustrated throughout with graph-based examples.
The book is divided into three parts. Part I presents the fundamental theoretical foundations of combinatorial game theory. Part II explores their applications to recently studied games on graphs, and Part III provides a summary of the theory of partizan games in the normal variant. Readers will find coverage of the Sprague-Grundy theory for impartial games, extremal combinatorics in game settings, computational complexity of games, convexity games on graphs, domination games, cops-and-robber games, as well as Conway's theory of partizan games and surreal numbers. Beyond its introductory material, the book also brings together several active research topics that are typically scattered across the literature, such as graph coloring games, graph convexity games, and connectivity games.
Although primarily designed for undergraduate students, the book's more advanced results will also be valuable to graduate students and researchers working in the area.
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Persons
Samuel N. Araújo is a Professor at the Federal Institute of Education, Science, and Technology of Ceará (IFCE), Brazil. He holds a PhD in Computer Science (2023) from the Federal University of Ceará, with visiting periods at INRIA, France (2024), and at the University of Massachusetts, USA (2012-2013). His research focuses on combinatorial game theory and computational complexity.
Nicolas A. Martins is a Professor at the University of International Integration of Afro-Brazilian Lusophony (UNILAB), Brazil. He holds a PhD in Computer Science (2018) from the Federal University of Ceará. His research interests include graph theory, graph coloring, graph decomposition, computational complexity, and algorithms.
Nicolas Nisse is a Research Director at INRIA and Université Côte d'Azur, France. He received his Master's and PhD degrees (2007) from the LRI, University of Paris 11, France, and completed a post-doctoral fellowship (2008) at the University of Chile. His main research interests concern the design of efficient algorithms for solving problems arising in telecommunications networks.
Rudini M. Sampaio is a Full Professor at the Federal University of Ceará, Brazil. He completed his PhD studies in Computer Science (2008) at the University of São Paulo, and earned his Master's degree (2000) from the Federal University of Ceará. His research activities focus on combinatorics, graph theory, algorithms, and computational complexity.
Content
Introduction to combinatorial games.- Sprague-Grundy theory of impartial games.- Extremal combinatorics for games.- Positional games.- Computational complexity of games.- Convexity games in graphs.- Coloring games in graphs.- Domination games in graphs.- Cops and robber games on graphs.- Conway's theory of partizan games.- Appendix.