Introduction to Graph Convexity
An Algorithmic Approach
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Beschreibung
This book focuses on the computational aspects of graph convexity, with a particular emphasis on path convexity within graphs. It provides a thoughtful introduction to this emerging research field, which originated by adapting concepts from convex geometry to combinatorics and has experienced substantial growth.
The book starts with an introduction of fundamental convexity concepts and then proceeds to discuss convexity parameters. These parameters fall into two categories: one derived from abstract convexity studies and another motivated by computational complexity. Subsequent chapters explore geometric convexity within graphs, examining various graph classes such as interval graphs, proper interval graphs, cographs, chordal graphs, and strongly chordal graphs. The text concludes with a study of the computation of convexity parameters across different convexity types, including practical applications in areas like game theory.
Compact and straightforward, this work serves as an ideal entry point for students and researchers interested in pursuing further research in the field of convexity.
The English translation of this book, originally in Portuguese, was facilitated by artificial intelligence. The content was later revised by the authors for accuracy.
This book focuses on the computational aspects of graph convexity, with a particular emphasis on path convexity within graphs. It provides a thoughtful introduction to this emerging research field, which originated by adapting concepts from convex geometry to combinatorics and has experienced substantial growth.
The book starts with an introduction of fundamental convexity concepts and then proceeds to discuss convexity parameters. These parameters fall into two categories: one derived from abstract convexity studies and another motivated by computational complexity. Subsequent chapters explore geometric convexity within graphs, examining various graph classes such as interval graphs, proper interval graphs, cographs, chordal graphs, and strongly chordal graphs. The text concludes with a study of the computation of convexity parameters across different convexity types, including practical applications in areas like game theory.
Compact and straightforward, this work serves as an ideal entry point for students and researchers interested in pursuing further research in the field of convexity.
The English translation of this book, originally in Portuguese, was facilitated by artificial intelligence. The content was later revised by the authors for accuracy.
Offers a comprehensive introduction to the computational aspects of graph convexity Covers convexity parameters in both abstract and computational contexts Examines various graph classes, including interval graphs, cographs, and chordal graphs
Autor*in
Júlio Araújo
Themen in »Introduction to Graph Convexity«
graph convexity convexity parameters computational complexity abstract convexity convexity games convex geometries in graphs geodesic convexity diffusion models in graphs Hull number Carathéodory number Radon number Helly number