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Graphs & Digraphs, Fourth Edition 4th New edition [Kietas viršelis]

4.11/5 (19 ratings by Goodreads)
(Western Michigan University, Kalamazoo, USA), (Western Michigan University, Kalamazoo, USA), (Western Michigan University, Kalamazoo, USA)
  • Formatas: Hardback, 386 pages, aukštis x plotis: 235x156 mm, weight: 703 g, 163 Illustrations, black and white
  • Serija: Textbooks in Mathematics
  • Išleidimo metai: 28-Oct-2004
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1584883901
  • ISBN-13: 9781584883906
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 386 pages, aukštis x plotis: 235x156 mm, weight: 703 g, 163 Illustrations, black and white
  • Serija: Textbooks in Mathematics
  • Išleidimo metai: 28-Oct-2004
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1584883901
  • ISBN-13: 9781584883906
Kitos knygos pagal šią temą:
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 The authors have added discussions on topics of increasing interest, deleted outdated material, and judiciously augmented the Exercises sections to cover a range of problems that reach beyond the construction of proofs.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.
Preface to the fourth edition vii
Introduction to graphs and digraphs
1(32)
Graphs
1(11)
Degree sequences
12(4)
Connected graphs and distance
16(9)
Digraphs and multigraphs
25(8)
The structure of graphs
33(22)
Cut-vertices, bridges and blocks
33(5)
The automorphism group of a graph
38(5)
Cayley color graphs
43(4)
The reconstruction problem
47(8)
Trees and connectivity
55(30)
Elementary properties of trees
55(10)
Arboricity and vertex-arboricity
65(4)
Connectivity and edge-connectivity
69(6)
Menger's theorem
75(6)
The toughness of a graph
81(4)
Eulerian and hamiltonian graphs and digraphs
85(26)
Eulerian graphs and digraphs
85(7)
Hamiltonian graphs and digraphs
92(13)
Line graphs and powers of graphs
105(6)
Directed graphs
111(16)
Strong digraphs
111(2)
Tournaments
113(11)
Hamiltonian tournaments
124(3)
Planar graphs
127(34)
The Euler identity
127(8)
Characterizations of planar graphs
135(10)
Hamiltonian planar graphs
145(5)
Crossing number and thickness
150(11)
Graph embeddings
161(32)
The genus of a graph
161(9)
2-Cell embeddings of graphs
170(16)
The maximum genus of a graph
186(7)
Graph colorings
193(40)
Vertex colorings
193(16)
Edge colorings
209(7)
Map colorings and flows
216(17)
Matchings, factors and decompositions
233(40)
Matchings and independence in graphs
233(13)
Factorizations and decompositions
246(16)
Labelings of graphs
262(11)
Domination in graphs
273(20)
The domination number of a graph
273(10)
The independent domination number of a graph
283(3)
Other domination parameters
286(7)
Extremal graph theory
293(24)
Turan's theorem
293(5)
Extremal results on graphs
298(10)
Cages
308(9)
Ramsey theory
317(16)
Classical Ramsey numbers
317(6)
Generalized Ramsey theory
323(4)
Rainbow Ramsey numbers
327(6)
The probabilistic method in graph theory
333(14)
The probabilistic method
333(7)
Random graphs
340(7)
Glossary of symbols 347(4)
Graph theory books 1936--2004 351(8)
References 359(20)
Index 379