Combinatorics and Graph Theory (Undergraduate Texts in Mathematics) Book

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. The text is written in an enthusiastic and lively style. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The text is primarily directed toward upper-division undergraduate students, but lower-division undergraduates with a penchant for proof and graduate students seeking an introduction to these subjects will also find much of interest. John Harris did his undergraduate work at Furman University, and he received his Ph.D. from Emory University. He has taught at Appalachian State University and at Furman. His primary mathematical interest is finite graph theory, focusing mainly on subgraphs, paths, and cycles. Jeff Hirst is a mathematical logician and has published a number of papers analyzing the logical strength of theorems of infinite graph theory and combinatorics. He received his B.A. and M.A. from the University of Kansas, and his Ph.D. from the Pennsylvania State University. He has taught at the Ohio State University and Appalachian State University. Michael Mossinghoff received his undergraduate degree from Texas A & M University, his M.S. in computer science from Stanford University, and his Ph.D. in mathematics from the University of Texas at Austin. He has taught at Appalachian State University and UCLA. His research concerns analytic and algorithmic problems in number theory and combinatorics.Read More