About the Book
Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory.
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.
Table of Contents:
Introduction. Connected Graphs and Distance. Trees. Connectivity. Eulerian Graphs. Hamiltonian Graphs. Digraphs. Flows in Networks. Automorphisms and Reconstruction. Planar Graphs. Nonplanar Graphs. Matchings, Independence and Domination. Factorization and Decomposition. Vertex Colorings. Perfect Graphs and List Colorings. Map Colorings. Edge Colorings. Nowhere-Zero Flows, List Edge Colorings. Extremal Graph Theory. Ramsey Theory. The Probabilistic Method.
About the Author :
Gary Chartrand is a professor emeritus of mathematics at Western Michigan University, Kalamazoo, Michigan, USA. Linda Lesniak, a professor emeritus of mathematics from Drew University, Madison, New Jersey, USA, is currently a visiting mathematician at Western Michigan University, Kalamazoo, Michigan, USA. Ping Zhang is a professor of mathematics at Western Michigan University, Kalamazoo, Michigan, USA. All three have authored or coauthored many textbooks in mathematics and numerous research articles in graph theory.
Review :
Praise for the Previous Edition
"Now in its fifth edition, its success as a textbook is indicative of its quality and its clarity of presentation. … The authors also describe the fascinating history behind some of the key problems in graph theory and, to a lesser extent, their applications. This book describes the key concepts you need to get started in graph theory. … It provides all you might need to know about graph embeddings and graph colorings. Moreover, it analyzes many other topics that more general discrete mathematics monographs do not always cover, such as network flows, minimum cuts, matchings, factorization, decomposition, and even extremal graph theory. … This thorough textbook includes hundreds of exercises at the end of each section. Hints and solutions for odd-numbered exercises are included in the appendix, making it especially suitable for self-learning."
—Fernando Berzal, Computing Reviews, September 2011
"As with the earlier editions, the current text emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge. … The fifth edition continues and extends these fine traditions."
—Arthur T. White, Zentralblatt MATH 1211
Praise for the Previous Edition
"Now in its fifth edition, its success as a textbook is indicative of its quality and its clarity of presentation. … The authors also describe the fascinating history behind some of the key problems in graph theory and, to a lesser extent, their applications. This book describes the key concepts you need to get started in graph theory. … It provides all you might need to know about graph embeddings and graph colorings. Moreover, it analyzes many other topics that more general discrete mathematics monographs do not always cover, such as network flows, minimum cuts, matchings, factorization, decomposition, and even extremal graph theory. … This thorough textbook includes hundreds of exercises at the end of each section. Hints and solutions for odd-numbered exercises are included in the appendix, making it especially suitable for self-learning."
—Fernando Berzal, Computing Reviews, September 2011
"As with the earlier editions, the current text emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge. … The fifth edition continues and extends these fine traditions."
—Arthur T. White, Zentralblatt MATH 1211
