Introduction to Graph Convexity An Algorithmic Approach

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.

Part I Fundamentals of Convexity in Graphs.- Basic Concepts of Convexity.- Convexity in Graphs.- Graph Convexity Parameters.- Convex Geometries in Graphs.- Part II Main Convexities and Applications.- P3 and P3* Convexities.- Geodesic Convexity.- Other Convexities.- Convexity in Oriental Graphs.- Applications in Graph Convexities.

Júlio Araújo is a Professor at the Federal University of Ceará, Brazil. He holds a Master's degree (2009) and a PhD (2012) in Computer Science from the same University, with post-doc studies at the Centre de Recherche INRIA Sophia Antipolis and the Laboratoire d'Informatique, Robotique et Microélectronique de Montpellier, both in France.

Mitre C. Dourado is an Associate Professor at the Federal University of Rio de Janeiro, Brazil. He did his Master's (2001) and PhD (2005) studies at the same University and did post-doc studies at the Université Paris 13 (Paris-Nord), France.

Fábio Protti is a Full Professor at the Fluminense Federal University, Brazil. He holds Master's (1993) and PhD (1998) degrees in Systems Engineering and Computing from the Federal University of Rio de Janeiro, Brazil. 

Rudini M. Sampaio is a Full Professor at the Federal University of Ceará, Brazil. He holds a Master's degree (2000) from the same university and a PhD (2008) from the University of São Paulo.