Combinatorics And Graph Theory A Comprehensive Introduction
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Combinatorics and Graph Theory
Author: John Harris
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-04-03
There are certain rules that one must abide by in order to create a successful sequel. — Randy Meeks, from the trailer to Scream 2 While we may not follow the precise rules that Mr. Meeks had in mind for s- cessful sequels, we have made a number of changes to the text in this second edition. In the new edition, we continue to introduce new topics with concrete - amples, we provide complete proofs of almost every result, and we preserve the book’sfriendlystyle andlivelypresentation,interspersingthetextwith occasional jokes and quotations. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order. Chapter 3, on in nite combinatorics and graphs, may also be studied independently, although many readers will want to investigate trees, matchings, and Ramsey theory for nite sets before exploring these topics for in nite sets in the third chapter. Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well. It assumes only familiarity with basic proof techniques, and some experience with matrices and in nite series. The second edition offersmany additionaltopics for use in the classroom or for independentstudy. Chapter 1 includesa new sectioncoveringdistance andrelated notions in graphs, following an expanded introductory section. This new section also introduces the adjacency matrix of a graph, and describes its connection to important features of the graph.
Combinatorics and Graph Theory: A Comprehensive Introduction
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-03-08
Embark on an intellectual journey through the captivating worlds of combinatorics and graph theory with "Combinatorics and Graph Theory: A Comprehensive Introduction." This comprehensive guide unveils the fundamental concepts, theorems, and applications of these interconnected disciplines, empowering readers to solve complex problems and gain a deeper understanding of the underlying patterns and structures that govern our world. Written in a clear and engaging manner, this book is designed for students, researchers, and enthusiasts alike. It begins with an exploration of discrete structures, delving into the intricacies of sets, relations, functions, and counting techniques. Readers are then guided through the fascinating realm of graphs, where they will discover their properties, algorithms, and diverse applications in various fields. As you progress through the chapters, you will encounter a wealth of captivating topics, including Ramsey theory, extremal combinatorics, coding theory, design theory, and much more. Each topic is presented with lucid explanations, insightful examples, and challenging exercises, fostering a deep understanding of the material. "Combinatorics and Graph Theory: A Comprehensive Introduction" is an invaluable resource for anyone seeking to master these fundamental disciplines. Its comprehensive coverage, engaging writing style, and abundance of practice problems make it an ideal companion for students, researchers, and enthusiasts alike. Whether you are seeking a solid foundation in combinatorics and graph theory, delving into the depths of these fields for research purposes, or simply seeking to expand your intellectual horizons, this book is your indispensable guide. Join us on this captivating journey as we unravel the mysteries of combinatorics and graph theory, unlocking new vistas of knowledge and igniting a passion for mathematical exploration. With its comprehensive coverage, clear explanations, and engaging examples, "Combinatorics and Graph Theory: A Comprehensive Introduction" is the ultimate resource for anyone seeking to master these fundamental disciplines. Order your copy today and embark on an intellectual adventure that will transform your understanding of the world around you. If you like this book, write a review!
Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Second Edition)
Author: Miklos Bona
language: en
Publisher: World Scientific Publishing Company
Release Date: 2006-10-09
This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity.As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.