Graphs & digraphs
著者
書誌事項
Graphs & digraphs
Chapman & Hall/CRC, c2011
5th ed
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Graphs and digraphs
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Summary: "Written for advanced undergraduate and beginning graduate students, the fifth edition of this best-selling book provides a wide range of new examples along with historical discussions of mathematicians, problems, and conjectures. It features new and expanded coverage of such topics as toughness, graph minors, perfect graphs, list colorings, nowhere zero flows, list edge colorings, the road coloring problem, and the rainbow number of a graph. Additional applications, exercises, and examples illustrate the concepts and theorems"-- Provided by publisher
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
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 Hajos 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
Turan's Theorem
Cages
Ramsey Theory
Hints and Solutions to Odd-Numbered Exercises
Bibliography
Index of Names
Index of Mathematical Terms
List of Symbols
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