Combinatorics and Graph Theory (Undergraduate Texts in Mathematics)

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: (1) New sections in graph theory on distance, Eulerian trails, and hamiltonian paths. (2) New material on partitions, multinomial coefficients, and the pigeonhole principle. (3) Expanded coverage of Pólya Theory to include de Bruijn’s method for counting arrangements when a second symmetry group acts on the set of allowed colors. (4) Topics in combinatorial geometry, including Erdos and Szekeres’ development of Ramsey Theory in a problem about convex polygons determined by sets of points. (5) Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable. (6) 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