Combinatorics and Graph Theory (Springer Undergraduate Texts in Mathematics and Technology)

This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA.

Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey theory.

Chapter 2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, Pólya theory, the stable marriage problem, and several important classes of numbers.

Chapter 3 presents infinite pigeonhole principles, König's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory.