Graphs & Digraphs, Fifth Edition
Taylor & Francis Inc (Verlag)
978-1-4398-2627-0 (ISBN)
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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.
Gary Chartrand is a professor emeritus of mathematics at Western Michigan University. Linda Lesniak is a professor emeritus of mathematics at Drew University. Ping Zhang is a professor of mathematics at Western Michigan University. All three have authored or co-authored many textbooks in mathematics and numerous research articles in graph theory.
Introduction to Graphs
Graphs and Subgraphs
Degree Sequences
Connected Graphs and Distance
Multigraphs and Digraphs
Trees and Connectivity
Nonseparable Graphs
Trees
Spanning Trees
Connectivity and Edge-Connectivity
Menger’s Theorem
Eulerian and Hamiltonian Graphs
Eulerian Graphs
Hamiltonian Graphs
Powers of Graphs and Line Graphs
Digraphs
Strong Digraphs
Tournaments
Flows in Networks
Graphs: History and Symmetry
Some Historical Figures of Graph Theory
The Automorphism Group of a Graph
Cayley Color Graphs
The Reconstruction Problem
Planar Graphs
The Euler Identity
Planarity versus Nonplanarity
The Crossing Number of a Graph
Hamiltonian Planar Graphs
Graph Embeddings
The Genus of a Graph
2-Cell Embeddings of Graphs
The Maximum Genus of a Graph
The Graph Minor Theorem
Vertex Colorings
The Chromatic Number of a Graph
Color-Critical Graphs
Bounds for the Chromatic Number
Perfect Graphs
List Colorings
Map Colorings
The Four Color Problem
Colorings of Planar Graphs
The Conjectures of Hajós and Hadwiger
Chromatic Polynomials
The Heawood Map-Coloring Problem
Matchings, Factorization, and Domination
Matchings and Independence in Graphs
Factorization
Decomposition and Graceful Graphs
Domination
Edge Colorings
Chromatic Index and Vizing’s Theorem
Class One and Class Two Graphs
Tait Colorings
Nowhere-Zero Flows
List Edge Colorings and Total Colorings
Extremal Graph Theory
Turán’s Theorem
Cages
Ramsey Theory
Hints and Solutions to Odd-Numbered Exercises
Bibliography
Index of Names
Index of Mathematical Terms
List of Symbols
| Erscheint lt. Verlag | 25.10.2010 |
|---|---|
| Reihe/Serie | Textbooks in Mathematics |
| Zusatzinfo | 1000+; 340 Illustrations, black and white |
| Verlagsort | Washington |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 975 g |
| Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| ISBN-10 | 1-4398-2627-7 / 1439826277 |
| ISBN-13 | 978-1-4398-2627-0 / 9781439826270 |
| Zustand | Neuware |
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