This is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods.

Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of life’s problems—problems that previously seemed hopeless. Review from the first edition: The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art...Keep this book at hand as you plan your next problem solving seminar. —The American Mathematical Monthly

This fifth edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications. Excellent exercise sets allow students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study.

This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds