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E-raamat: Tour through Graph Theory [Taylor & Francis e-raamat]

  • Formaat: 320 pages, 77 Tables, black and white; 306 Illustrations, black and white
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 24-Oct-2017
  • Kirjastus: CRC Press
  • ISBN-13: 9781315116839
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  • Taylor & Francis e-raamat
  • Hind: 244,66 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 349,51 €
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Tour through Graph TheorySuurem pilt
  • Formaat: 320 pages, 77 Tables, black and white; 306 Illustrations, black and white
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 24-Oct-2017
  • Kirjastus: CRC Press
  • ISBN-13: 9781315116839
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781315116839
A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book inspires readers to learn by working through examples, drawing graphs and exploring concepts.

This book distinguishes itself from others covering the same topic. It strikes a balance of focusing on accessible problems for non-mathematical students while providing enough material for a semester-long course.











Employs graph theory to teach mathematical reasoning





Expressly written for non-mathematical students





Promotes critical thinking and problem solving





Provides rich examples and clear explanations without using proofs
Preface xiii
1 Eulerian Tours
1(34)
1.1 Konigsberg Bridge Problem
1(1)
1.2 Introduction to Graph Models
2(4)
1.3 Touring a Graph
6(6)
1.4 Eulerian Circuit Algorithms
12(7)
Fleury's Algorithm
12(4)
Hierholzer's Algorithm
16(3)
1.5 Eulerization
19(8)
Chinese Postman Problem
24(3)
1.6 Exercises
27(8)
2 Hamiltonian Cycles
35(46)
2.1 Conditions for Existence
36(5)
2.2 Traveling Salesman Problem
41(22)
Brute Force
42(5)
Nearest Neighbor
47(4)
Cheapest Link
51(3)
Nearest Insertion
54(9)
2.3 Digraphs
63(9)
Asymmetric Traveling Salesman Problem
65(7)
2.4 Exercises
72(9)
3 Paths
81(28)
3.1 Shortest Paths
81(12)
Dijkstra's Algorithm
82(9)
Chinese Postman Problem Revisited
91(2)
3.2 Project Scheduling
93(10)
Critical Paths
97(6)
3.3 Exercises
103(6)
4 Trees and Networks
109(42)
4.1 Trees
109(4)
4.2 Spanning Trees
113(17)
Kruskal's Algorithm
115(8)
Prim's Algorithm
123(7)
4.3 Shortest Networks
130(10)
Steiner Trees
136(4)
4.4 Traveling Salesman Problem Revisited
140(4)
4.5 Exercises
144(7)
5 Matching
151(38)
5.1 Bipartite Graphs
152(2)
5.2 Matching Terminology and Strategies
154(14)
Augmenting Paths and Vertex Covers
159(9)
5.3 Stable Marriages
168(8)
Unacceptable Partners
173(3)
5.4 Matchings in Non-Bipartite Graphs
176(4)
Stable Roommates
178(2)
5.5 Exercises
180(9)
6 Graph Coloring
189(38)
6.1 Four Color Theorem
189(3)
6.2 Coloring Bounds
192(4)
6.3 Coloring Strategies
196(11)
General Strategies
196(4)
On-line Coloring
200(7)
6.4 Perfect Graphs
207(9)
Interval Graphs
207(6)
Tolerance Graphs
213(3)
6.5 Weighted Coloring
216(5)
6.6 Exercises
221(6)
7 Additional Topics
227(58)
7.1 Algorithm Complexity
227(5)
Exercises
232(1)
7.2 Graph Isomorphism
232(4)
Exercises
235(1)
7.3 Tournaments
236(9)
Exercises
245(1)
7.4 Flow and Capacity
245(11)
Exercises
255(1)
7.5 Rooted Trees
256(9)
Depth-First Search Tree
258(3)
Breadth-First Search Tree
261(3)
Exercises
264(1)
7.6 Planarity
265(9)
Exercises
272(2)
7.7 Edge-Coloring
274(11)
Ramsey Numbers
281(3)
Exercises
284(1)
Appendix 285(1)
Creating a Triangle 285(1)
Finding Angle Measure 285(1)
Finding the Fermat Point 286(1)
Other Items 286(1)
Exercises 287(2)
Selected Answers and Solutions 289(6)
Bibliography 295(4)
Image Credits 299(2)
Index 301
Dr. Karin R. Saoub is an associate professor of Mathematics at Roanoke College in Salem, Virginia. She received her PhD in Mathematics from Arizona State University and a Bachelor of Arts degree from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs.
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