These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

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This book covers a wide variety of topics in combinatorics and graph theory. 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 second edition includes many new topics and features:

• New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths.

• New material on partitions, multinomial coefficients, and the pigeonhole principle.

• Expanded coverage of P�lya Theory to include de Bruijn’s method for counting arrangements when a second symmetry group acts on the set of allowed colors.

• Topics in combinatorial geometry, including Erdos and Szekeres’ development of Ramsey Theory in a problem about convex polygons determined by sets of points.

• Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable.

• Numerous new exercises throughout the book.

About the First Edition:

". . . this is what a textbook should be! The book is comprehensive without being overwhelming, the proofs are elegant, clear and short, and the examples are well picked."

— Ioana Mihaila, MAA Reviews

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