Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Third Edition)

This textbook serves as an introduction to combinatorics over one or two semesters, featuring a variety of problems, classic topics, and recent advancements in enumeration and graph theory.

Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory (Third Edition) serves as a comprehensive textbook for an introductory combinatorics course, suitable for one or two semesters. The book is designed to cater to a wide range of learners, featuring a diverse array of problems that span from basic exercises to more challenging research questions. Each section includes additional exercises that introduce material not covered in the main text, offering instructors the flexibility to tailor their courses according to their teaching priorities.

This edition continues the tradition of its predecessors by guiding readers through essential topics in combinatorial enumeration and graph theory. It emphasizes foundational techniques while also highlighting recent advancements in the field. The book aims to make complex ideas accessible to dedicated undergraduates, covering key concepts such as the twelvefold way, cycles in permutations, inclusion-exclusion principles, and various types of graphs and trees.

In addition to the core topics, the book introduces advanced subjects like Ramsey theory, pattern avoidance, the probabilistic method, and the theory of designs, which are new to this edition. The authors strive to create an engaging learning experience, encouraging students to delve deeper into combinatorics. For instructors who choose this text, a Solution Manual is available upon request, ensuring they have the resources needed to support their teaching effectively.