Graphs & Digraphs, Fourth Edition (Textbooks in Mathematics)

Zhang, Ping,Lesniak, Linda,Chartrand, Gary

ISBN 10: 1584883901 / ISBN 13: 9781584883906

Editore: Chapman and Hall/CRC, 2004

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Dati bibliografici

• Titolo: Graphs & Digraphs, Fourth Edition (Textbooks in Mathematics)
• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 1584883901
• ISBN 13: 9781584883906
• Rilegatura: Hardcover
• Edizione: quarta edizione
• Condizione: Good

Descrizione articolo

Riassunto

With a growing range of applications in fields from computer science to chemistry and communications networks, graph theory has enjoyed a rapid increase of interest and widespread recognition as an important area of mathematics. Through more than 20 years of publication, Graphs & Digraphs has remained a popular point of entry to the field, and through its various editions, has evolved with the field from a purely mathematical treatment to one that also addresses the mathematical needs of computer scientists.

Carefully updated, streamlined, and enhanced with new features, Graphs & Digraphs, Fourth Edition reflects many of the developments in graph theory that have emerged in recent years. The authors have added discussions on topics of increasing interest, deleted outdated material, and judiciously augmented the Exercises sections to cover a range of problems that reach beyond the construction of proofs.

New in the Fourth Edition:

Expanded treatment of Ramsey theory

Major revisions to the material on domination and distance

New material on list colorings that includes interesting recent results

A solutions manual covering many of the exercises available to instructors with qualifying course adoptions

A comprehensive bibliography including an updated list of graph theory books

Every edition of Graphs & Digraphs has been unique in its reflection the subject as one that is important, intriguing, and most of all beautiful. The fourth edition continues that tradition, offering a comprehensive, tightly integrated, and up-to-date introduction that imparts an appreciation as well as a solid understanding of the material.

Contenuti

INTRODUCTION TO GRAPHS AND DIGRAPHS
Graphs
Degree Sequences
Connected Graphs and Distance
Digraphs and Multigraphs
THE STRUCTURE OF GRAPHS
Cut-Vertices, Bridges and Blocks
The Automorphism Group of a Graph
Cayley Color Graphs
The Reconstruction Problem
TREES AND CONNECTIVITY
Elementary Properties of Trees
Arboricity and Vertex-Arboricity
Connectivity and Edge-Connectivity
Menger's Theorem
The Toughness of a Graph
EULERIAN AND HAMILTONIAN GRAPHS AND DIGRAPHS
Eulerian Graphs and Digraphs
Hamiltonian Graphs and Digraphs
Line Graphs and Powers of Graphs
DIRECTED GRAPHS
Strong Digraphs
Tournaments
Hamiltonian Tournaments
PLANAR GRAPHS
The Euler Identity
Characterizations of Planar Graphs
Hamiltonian Planar Graphs
Crossing Number and Thickness
GRAPH EMBEDDINGS
The Genus of a Graph
2-Cell Embeddings of Graphs
The Maximum Genus of a Graph
GRAPH COLORINGS
Vertex Colorings
Edge Colorings
Map Colorings and Flows
MATCHINGS, FACTORS AND DECOMPOSITIONS
Matchings and Independence in Graphs
Factorizations and Decompositions
Labelings of Graphs
DOMINATION IN GRAPHS
The Domination Number of a Graph
The Independent Domination Number of a Graph
Other Domination Parameters
EXTREMAL GRAPH THEORY
Tura´n's Theorem
Extremal Results on Graphs
Cages
RAMSEY THEORY
Classical Ramsey Numbers
Generalized Ramsey Theory
Rainbow Ramsey Numbers
THE PROBABILISTIC METHOD IN GRAPH THEORY
The Probabilistic Method
Random Graphs

Glossary of Symbols
Graph Theory Books
References