A walk through combinatorics

"This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs."--

13.1 Ramsey Theory for Finite Graphs

Intro; Contents; Foreword; Preface; Acknowledgments; Chapter 1 Seven Is More Than Six. The Pigeon-Hole Principle; 1.1 The Basic Pigeon-Hole Principle; 1.2 The Generalized Pigeon-Hole Principle; Exercises; Supplementary Exercises; Solutions to Exercises; Chapter 2 One Step at a Time. The Method of Mathematical Induction; 2.1 Weak Induction; 2.2 Strong Induction; Exercises; Supplementary Exercises; Solutions to Exercises; Chapter 3 There Are A Lot Of Them. Elementary Counting Problems; 3.1 Permutations; 3.2 Strings over a Finite Alphabet; 3.3 Choice Problems; Exercises; Supplementary Exercises

Solutions to ExercisesChapter 4 No Matter How You Slice It. The Binomial Theorem and Related Identities; 4.1 The Binomial Theorem; 4.2 The Multinomial Theorem; 4.3 When the Exponent Is Not a Positive Integer; Exercises; Supplementary Exercises; Solutions to Exercises; Chapter 5 Divide and Conquer. Partitions; 5.1 Compositions; 5.2 Set Partitions; 5.3 Integer Partitions; Exercises; Supplementary Exercises; Solutions to Exercises; Chapter 6 Not So Vicious Cycles. Cycles in Permutations; 6.1 Cycles in Permutations; 6.2 Permutations with Restricted Cycle Structure; Exercises

Supplementary Exerci…