Maximal Planar Graph Theory and the Four-Color Conjecture

This open access book integrates foundational principles with advanced methodologies concerning maximal planar graphs. It offers readers an exceptional examination of graph structures, chromatic polynomials, and the construction and proof techniques of the Four-Color Conjecture. It is tailored for researchers, educators, and students involved in graph theory, combinatorics, and computational mathematics.

The book consists of nine meticulously developed chapters. It starts with fundamental concepts in graph theory and then advances to pioneering computational proofs and recursive formulas of the chromatic number related to maximal planar graphs. Notable features include comprehensive discharging techniques, innovative approaches for constructing graphs of various orders, and groundbreaking conjectures concerning tree-colorability and unique four-colorability. The concluding chapter introduces Kempe's changes, offering new insights into the dynamics of graph coloring.

Whether you are an academic enhancing your theoretical knowledge or a student searching for clear explanations for complex concepts, this book provides essential tools for navigating and addressing some of the most intricate challenges in graph theory. Its rigorous analysis and computational techniques equip readers with the necessary skills to engage deeply with maximal planar graph problems, making it an indispensable resource for advancing research and practical applications.

No prior knowledge is necessary; however, a foundational understanding of graph theory is advised. This opportunity presents a chance to explore innovative perspectives and methodologies that expand the horizons of mathematical inquiry and proof development.

This book is open access, which means that you have free and unlimited access The first comprehensive book was dedicated to studying maximal planar graphs Systematically introduces the structures and constructions of maximal planar graphs Includes over 200 graphs to illustrate definitions, concepts, and proofs of theorems

Autorentext

Jin Xu is a tenured professor and PhD supervisor at Peking University, holding dual doctorates in science and engineering. With over thirty years of academic and research experience, Dr. Xu specializes in graph theory, biological computing, and neural networks—fields directly tied to the themes explored in this book.

An accomplished scholar, Dr. Xu has authored over 200 SCI-indexed papers as the first or corresponding author and led ten prestigious national research projects, including the NSFC, ‘973,’ and ‘863’ initiatives. His groundbreaking work has earned the Second Prize in the National Natural Science Award and multiple First Prizes in the Natural Science Awards from the Ministry of Education and Hubei Province.

Inhalt

Chapter 1 Graph Theory Fundamentals.- Chapter 2 Discharging and Structure of Maximal Planar Graphs.- Chapter 3 Computer-Based Proofs of Four Color Conjecture.- Chapter 4 Construction of Maximal Planar Graphs with the same order.- Chapter 5 Construction of Maximal Planar Graphs with the different order.- Chapter 6 Generating System of Maximal Planar Graphs.- Chapter 7 Recursion Formulae of Chromatic Polynomial and Four-Color Conjecture.- Chapter 8 Purely Tree-colorable and Uniquely 4-Colorable Maximal Planar Graph Conjectures.- Chapter 9 Kempe Change.