Problems in Combinatorics and Graph Theory (Wiley Series in Discrete Mathematics and Optimization)

Covers the most important combinatorial structures and techniques. This is a book of problems and solutions which range in difficulty and scope from the elementary/student-oriented to open questions at the research level. Each problem is accompanied by a complete and detailed solution together with appropriate references to the mathematical literature, helping the reader not only to learn but to apply the relevant discrete methods. The text is unique in its range and variety -- some problems include straightforward manipulations while others are more complicated and require insights and a solid foundation of combinatorics and/or graph theory. Includes a dictionary of terms that makes many of the challenging problems accessible to those whose mathematical education is limited to highschool algebra. Part 1: Statement Of Problems -- Combinatorial Identities -- The Principle Of Inclusion And Exclusion: Inversion Formulas -- Stirling, Bell, Fibonacci, And Catalan Numbers -- Problems In Combinatorial Set Theory -- Partitions Of Integers -- Trees -- Parity -- Connectedness -- Extremal Problems For Graphs And Networks -- Coloring Problems -- Hamiltonian Problems -- Permutations -- The Number Of Classes Of Configurations Relative To A Group Of Permutations -- Problems Of Ramsey Type -- Part 2: Solutions. Ioan Tomescu ; Translated From Romanian By Robert A. Melter. Translation Of: Probleme De Combinatorică Și Teoria Grafurilor. A Wiley-interscience Publication. Revisions In The Original Romanian Edition Have Been Made, And About 60 New Problems And Solutions Have Been Added--pref. Bibliography: P. 335. Title Preface Contents Glossary of Terms Used Part I: Statements of Problems 1. Combinatorial Identities 2. The Principle of Inclusion and Exclusion; Inversion Formulas 3. Stirling, Bell, Fibonacci, and Catalan Numbers 4. Problems in Combinatorial Set Theory 5. Partitions of Integers 6. Trees 7. Parity 8. Connectedness 9. Extremal Problems for Graphs and Networks 10. Coloring Problems 11. Hamiltonian Problems 12. Permutations 13. The Number of Classes of Configurations Relative to a Group of Permutations 14. Problems of Ramsey Type Part II: Solutions Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Bibliography Three hundred and sixty-nine problems with fully worked solutions for courses in computer science, combinatorics, and graph theory, designed to provide graded practice to students with as little as a high school algebra background.