Gary Chartrand

Albert D. Polimeni

Zhang, Ping

A Transition to Advanced Mathematics (2nd Edition)

Mathematical Proofs

Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. 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.

Introductory Graph Theory

Ping Zhang

Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET: For all readers interested in advanced mathematics and logic.

A Transition to Advanced Mathematics

Normal 0 false false false 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.

With Chromatic Graph Theory, Second Edition, the authors present 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. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also 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. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition

Chromatic Graph Theory

Linda Lesniak

Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics. 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.

Graphs & Digraphs, Fifth Edition

Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.

A First Course in Graph Theory

Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. 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.

Yousef Alavi

Don R. Lick

C. E. Wall

An applications-oriented text detailing the latest research in graph theory and computer science. Leading contributors cover such important topics as: tiling problems and graph factors; partitioning the nodes of a graph; diameter vulnerability in networks; edge-disjoint Hamiltonian cycles; the cochromatic number of graphs in a switching sequence; and more.

Graph Theory with Applications to Algorithms and Computer Science

"Unreasonable Leadership provides a blueprint of how to lead and forge change in all types of economic environments. Gary Chartrand's powerful message of redefining the game, creating new pathways where there are none, leading without fear and mobilizing teams to coalesce around a goal is a timeless tool and is a must read for all who would call themselves leaders." 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.

Gary Chartrand

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