Combinatorics and graph theory / John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff

This undergraduate textbook contains three chapters: Graph Theory, Combinatorics, and Infinite Combinatorics and Graphs. Chapter 1 contains sections on Introductory Concepts; Distance in Graphs; Trees; Trails, Circuits, Paths, and Cycles; Planarity; Colorings; Matchings; and Ramsey Theory. Chapter 2 contains five short sections on Some Essential Problems; Binomial Coefficients; Multinomial Coefficients; The Pigeonhole Principle; and The Principle of Inclusion and Exclusion; and five longer sections on Generating Functions, Pólya’s Theory of Counting; More Numbers; Stable Marriage; and Combinatorial Geometry. Chapter 3 contains seven short sections on Pigeons and Trees; Ramsey Revisited; The Return of der König; Weakly Compact Cardinals; Finite Combinatorics with Infinite Consequences; k-critical Linear Orderings; and Points of Departure; and four longer sections on Zermelo, Fraenkel, and Axiom of Choice; Ordinals, Cardinals, and Many Pigeons; Incompleteness and Cardinals; and Infinite Marriage Problems.

There is a short section on References in each chapter introducing briefly other books dealing with the topics covered in the respective chapter. A full list of 293 references, about 550 exercises and an index with 13 pages are also provided. (Zentralblatt)