Fully updated and thoughtfully reorganized to make reading and locating material easier for instructors and students, the Sixth Edition of this bestselling, classroom-tested text:Adds more than 160 new exercises Presents many new concepts, theorems, and examples Includes recent major contributions to long-standing conjectures such as the Hamiltonian Factorization Conjecture, 1-Factorization Conjecture, and Alspach’s Conjecture on graph decompositions Supplies a proof of the perfect graph theorem Features a revised chapter on the probabilistic method in graph theory with many results integrated throughout the text
At the end of the book are indices and lists of mathematicians’ names, terms, symbols, and useful references. There is also a section giving hints and solutions to all odd-numbered exercises. A complete solutions manual is available with qualifying course adoption.
Graphs & Digraphs, Sixth Edition remains the consummate text for an advanced undergraduate level or introductory graduate level course or two-semester sequence on graph theory, exploring the subject’s fascinating history while covering a host of interesting problems and diverse applications.
Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics.
Ten major topics — profusely illustrated — include: Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party Problems, Digraphs and Mathematical Models, Games and Puzzles, Graphs and Social Psychology, Planar Graphs and Coloring Problems, and Graphs and Other Mathematics.
A useful Appendix covers Sets, Relations, Functions, and Proofs, and a section devoted to exercises — with answers, hints, and solutions — is especially valuable to anyone encountering graph theory for the first time.
Undergraduate mathematics students at every level, puzzlists, and mathematical hobbyists will find well-organized coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book.
Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.
This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex colorings.
With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory.
Optional sections designated as "excursion" and "exploration" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three appendixes review important facts about sets and logic, equivalence relations and functions, and the methods of proof. The text concludes with solutions or hints for odd-numbered exercises, in addition to references, indexes, and a list of symbols.
This highly versatile text provides mathematical background used in a wide variety of disciplines, including mathematics and mathematics education, computer science, biology, chemistry, engineering, communications, and business.
Some of the major features and strengths of this textbook
More than 1,600 exercises, ranging from elementary to challenging, are included with hints/answers to all odd-numbered exercises.
Descriptions of proof techniques are accessible and lively.
Students benefit from the historical discussions throughout the textbook.
New to the Fifth Edition
New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings New examples, figures, and applications to illustrate concepts and theorems Expanded historical discussions of well-known mathematicians and problems More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book Reorganization of sections into subsections to make the material easier to read Bolded definitions of terms, making them easier to locate
Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject’s fascinating history and presents a host of interesting problems and diverse applications.
Carla Harris, author of Expect To Win
"Unreasonable Leadership should be required reading in every business school. What Gary Chartrand did to build Acosta into a industry leading sales and Marketing Juggernaut is simply remarkable and so is this book."
Jon Gordon, Best-selling author of The Energy Bus and Soup
"This is a smart, thought-provoking approach to leadership and how to create the ideal environment for bringing about positive change and achieving meaningful results."
Mitt Romney, Former Governor of Massachusetts
Gary Chartrand's Unreasonable Leadership provides a blueprint for leaders who are driving change not only in the corporate sector but in the social sector as well. Gary describes what it takes to be a true pioneer, to achieve unprecedented, ground breaking results despite the complexity of the work and the enormity of the challenges. We've learned through Teach for America that Unreasonable Leadership is exactly what is required to transform our entrenched public education systems.
Wendy Kopp, CEO and Founder of Teach For America
Achieving a vision that seemed nearly impossible, having the courage to make difficult decisions, and leading with conviction transformed a company and its entire industry. Unreasonable Leadership charts the growth of Acosta Sales and Marketing, a food brokerage firm that grew from a one-state operation employing 11 people to an international sales and marketing agency employing a staff of more than 16,000 in the US and Canada. During a 12-year span, company sales grew from $3 billion to $60 billion. How did this happen?
Acosta Chairman Gary Chartrand followed the advice of George Bernard Shaw: "All progress comes from unreasonable people." Chartrand's success as an unreasonable leader testifies to the value of setting a bold agenda, never being afraid to ask, and the critical importance of molding a corporate culture. His personal saga shows what can be accomplished no matter the odds of what "conventional wisdom" labels as impossible.