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Graph Theory and Its Applications 3rd edition [Kietas viršelis]

4.15/5 (40 ratings by Goodreads)
(Rollins College, Winter Park, Florida, USA), , (Columbia University, New York, USA)
  • Formatas: Hardback, 592 pages, aukštis x plotis: 254x178 mm, weight: 1226 g, 10 Tables, black and white; 905 Illustrations, black and white
  • Serija: Textbooks in Mathematics
  • Išleidimo metai: 06-Nov-2018
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1482249480
  • ISBN-13: 9781482249484
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 592 pages, aukštis x plotis: 254x178 mm, weight: 1226 g, 10 Tables, black and white; 905 Illustrations, black and white
  • Serija: Textbooks in Mathematics
  • Išleidimo metai: 06-Nov-2018
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1482249480
  • ISBN-13: 9781482249484
Kitos knygos pagal šią temą:
Graph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs.

The authors unparalleled treatment is an ideal text for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

Features of the Third Edition











Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions)





Provides better coverage of algorithms and algebraic and topological graph theory than any other text





Incorporates several levels of carefully designed exercises that promote student retention and develop and sharpen problem-solving skills





Includes supplementary exercises to develop problem-solving skills, solutions and hints, and a detailed appendix, which reviews the textbooks topics

About the Authors

Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory.

Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms.

Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.
Preface xi
Authors xiii
1 Introduction to Graph Models
1(58)
1.1 Graphs and Digraphs
2(13)
1.2 Common Families of Graphs
15(7)
1.3 Graph Modeling Applications
22(7)
1.4 Walks and Distance
29(11)
1.5 Paths, Cycles, and Trees
40(9)
1.6 Vertex and Edge Attributes: More Applications
49(4)
1.7 Supplementary Exercises
53(1)
Glossary
54(5)
2 Structure and Representation
59(62)
2.1 Graph Isomorphism
60(8)
2.2 Automorphisms and Symmetry
68(6)
2.3 Subgraphs
74(9)
2.4 Some Graph Operations
83(10)
2.5 Tests for Non-Isomorphism
93(7)
2.6 Matrix Representations
100(5)
2.7 More Graph Operations
105(8)
2.8 Supplementary Exercises
113(2)
Glossary
115(6)
3 Trees
121(52)
3.1 Characterizations and Properties of Trees
122(8)
3.2 Rooted Trees, Ordered Trees, and Binary Trees
130(8)
3.3 Binary-Tree Traversal
138(5)
3.4 Binary-Search Trees
143(5)
3.5 Huffman Trees and Optimal Prefix Codes
148(4)
3.6 Priority Trees
152(5)
3.7 Counting Labeled Trees: Prufer Encoding
157(6)
3.8 Counting Binary Trees: Catalan Recursion
163(2)
3.9 Supplementary Exercises
165(3)
Glossary
168(5)
4 Spanning Trees
173(56)
4.1 Tree Growing
174(7)
4.2 Depth-First and Breadth-First Search
181(5)
4.3 Minimum Spanning Trees and Shortest Paths
186(7)
4.4 Applications of Depth-First Search
193(8)
4.5 Cycles, Edge-Cuts, and Spanning Trees
201(6)
4.6 Graphs and Vector Spaces
207(11)
4.7 Matroids and the Greedy Algorithm
218(5)
4.8 Supplementary Exercises
223(1)
Glossary
224(5)
5 Connectivity
229(30)
5.1 Vertex- and Edge-Connectivity
230(5)
5.2 Constructing Reliable Networks
235(8)
5.3 Max-Min Duality and Menger's Theorems
243(9)
5.4 Block Decompositions
252(4)
5.5 Supplementary Exercises
256(1)
Glossary
257(2)
6 Optimal Graph Traversals
259(38)
6.1 Eulerian Trails and Tours'
260(4)
6.2 DeBruijn Sequences and Postman Problems
264(15)
6.3 Hamiltonian Paths and Cycles
279(5)
6.4 Gray Codes and Traveling Salesman Problems
284(10)
6.5 Supplementary Exercises
294(1)
Glossary
295(2)
7 Planarity and Kuratowski's Theorem
297(54)
7.1 Planar Drawings and Some Basic Surfaces
298(7)
7.2 Subdivision and Homeomorphism
305(4)
7.3 Extending Planar Drawings
309(7)
7.4 Kuratowski's Theorem
316(8)
7.5 Algebraic Tests for Planarity
324(13)
7.6 Planarity Algorithm
337(3)
7.7 Crossing Numbers and Thickness
340(5)
7.8 Supplementary Exercises
345(2)
Glossary
347(4)
8 Graph Colorings
351(48)
8.1 Vertex-Colorings
352(15)
8.2 Map-Colorings
367(7)
8.3 Edge-Colorings
374(14)
8.4 Factorization
388(5)
8.5 Supplementary Exercises
393(2)
Glossary
395(4)
9 Special Digraph Models
399(42)
9.1 Directed Paths and Mutual Reachability
400(11)
9.2 Digraphs as Models for Relations
411(6)
9.3 Tournaments
417(5)
9.4 Project Scheduling
422(7)
9.5 Finding the Strong Components of a Digraph
429(6)
9.6 Supplementary Exercises
435(1)
Glossary
436(5)
10 Network Flows and Applications
441(46)
10.1 Flows and Cuts in Networks
442(8)
10.2 Solving the Maximum-Flow Problem
450(10)
10.3 Flows and Connectivity
460(9)
10.4 Matchings, Transversals, and Vertex Covers
469(13)
10.5 Supplementary Exercises
482(1)
Glossary
483(4)
11 Graph Colorings and Symmetry
487(14)
11.1 Automorphisms of Simple Graphs
488(5)
11.2 Equivalence Classes of Colorings
493(6)
11.3 Supplementary Exercises
499(1)
Glossary
500(1)
A Appendix 501(14)
A.1 Logic Fundamentals
501(1)
A.2 Relations and Functions
502(3)
A.3 Some Basic Combinatorics
505(1)
A.4 Algebraic Structures
506(5)
A.5 Algorithmic Complexity
511(3)
A.6 Supplementary Reading
514(1)
B Bibliography 515(8)
B.1 General Reading
515(2)
B.2 References
517(6)
Solutions and Hints 523(40)
Index of Applications 563(2)
Index Of Algorithms 565(2)
General Index 567
Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory.

Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms.

Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.