Main subject categories: • Graph theoryMathematics Subject Classification (2000): • 05C Graph theory • 68R10 Graph theory (including graph drawing) in computer scienceGraph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics - computer science, combinatorial optimization, and operations research in particular - but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance.The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises - of varying levels of difficulty - are provided to help the reader master the techniques and reinforce their grasp of the material. A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters.

lgrsnf/M_Mathematics/MA_Algebra/MAc_Combinatorics/Bondy J.A., Murty U.S.R. Graph theory (GTM 244, Springer, 2008)(ISBN 1849966907)(O)(666s)_MAc_.pdf

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Graph Theory (Graduate Texts in Mathematics (244))

Graph Theory,Bondy, Adrian,Springer

Adrian Bondy, U.S.R Murty, J. A. Bondy

[by] J.A. Bondy [and], U.S.R. Murty

John Adrian Bondy; U S R Murty

Bondy, Adrian, Murty, U.S.R.

Bondy, J. A. (john Adrian)

Springer London Ltd

Springer Veralg

Graduate texts in mathematics -- 244, Graduate texts in mathematics -- 244., New York, New York State, 2010

1st Corrected ed. 2008. Corr. 3rd printing 2008, US, 2008

Graduate Texts in Mathematics, 244, New York, cop. 2010

Graduate texts in mathematics, 244, New York, NY, 2008

Softcover reprint of hardcover 1st ed. 2008, 2008

Graduate texts in mathematics, 244, London, 2008

United Kingdom and Ireland, United Kingdom

1 edition, December 11, 2007

2008, 2010

Kolxo3 -- 2011

lg513553

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Includes bibliographical references (p. 593-622) and index.

Bookmarks: p1 (p1): 1 Graphs
p2 (p39): 2 Subgraphs
p3 (p79): 3 Connected Graphs
p4 (p99): 4 Trees
p5 (p117): 5 Nonseparable Graphs
p6 (p135): 6 Tree-Search Algorithms
p7 (p157): 7 Flows in Networks
p8 (p173): 8 Complexity of Algorithms
p9 (p205): 9 Connectivity
p10 (p243): 10 Planar Graphs
p11 (p287): 11 The Four-Colour Problem
p12 (p295): 12 Stable Sets and Cliques
p13 (p329): 13 The Probabilistic Method
p14 (p357): 14 Vertex Colourings
p15 (p391): 15 Colourings of Maps
p16 (p413): 16 Matchings
p17 (p451): 17 Edge Colourings
p18 (p471): 18 Hamilton Cycles
p19 (p503): 19 Coverings and Packings in Directed Graphs
p20 (p527): 20 Electrical Networks
p21 (p557): 21 Integer Flows and Coverings
p22 (p583): Unsolved Problems
p23 (p593): References
p24 (p623): General Mathematical Notation
p25 (p625): Graph Parameters
p26 (p627): Operations and Relations
p27 (p629): Families of Graphs
p28 (p631): Structures
p29 (p633): Other Notation
p30 (p637): Index

Dedication......Page 6
Preface......Page 7
Contents......Page 11
1.1 Graphs and Their Representation......Page 13
1.2 Isomorphisms and Automorphisms......Page 24
1.3 Graphs Arising from Other Structures......Page 32
1.4 Constructing Graphs from Other Graphs......Page 41
1.5 Directed Graphs......Page 43
1.6 In.nite Graphs......Page 48
1.7 Related Reading......Page 49
2 Subgraphs......Page 51
2.1 Subgraphs and Supergraphs......Page 52
2.2 Spanning and Induced Subgraphs......Page 58
2.3 Modifying Graphs......Page 66
2.4 Decompositions and Coverings......Page 68
2.5 Edge Cuts and Bonds......Page 71
2.6 Even Subgraphs......Page 76
2.7 Graph Reconstruction......Page 78
2.8 Related Reading......Page 88
3.1 Walks and Connection......Page 91
3.2 Cut Edges......Page 97
3.3 Euler Tours......Page 98
3.4 Connection in Digraphs......Page 102
3.5 Cycle Double Covers......Page 105
3.6 Related Reading......Page 110
4.1 Forests and Trees......Page 111
4.2 Spanning Trees......Page 117
4.3 Fundamental Cycles and Bonds......Page 122
4.4 Related Reading......Page 126
5.1 Cut Vertices......Page 129
5.2 Separations and Blocks......Page 131
5.3 Ear Decompositions......Page 137
5.4 Directed Ear Decompositions......Page 141
5.5 Related Reading......Page 145
6.1 Tree-Search......Page 147
6.2 Minimum-Weight Spanning Trees......Page 157
6.3 Branching-Search......Page 161
6.4 Related Reading......Page 168
7.1 Transportation Networks......Page 169
7.2 The Max-Flow Min-Cut Theorem......Page 173
7.3 Arc-Disjoint Directed Paths......Page 179
7.4 Related Reading......Page 183
8.1 Computational Complexity......Page 185
8.2 Polynomial Reductions......Page 190
8.3 NP-Complete Problems......Page 192
8.4 Approximation Algorithms......Page 203
8.5 Greedy Heuristics......Page 205
8.6 Linear and Integer Programming......Page 209
8.7 Related Reading......Page 216
9.1 Vertex Connectivity......Page 217
9.2 The Fan Lemma......Page 225
9.3 Edge Connectivity......Page 228
9.4 Three-Connected Graphs......Page 231
9.5 Submodularity......Page 238
9.6 Gomory–Hu Trees......Page 243
9.7 Chordal Graphs......Page 247
9.8 Related Reading......Page 250
10.1 Plane and Planar Graphs......Page 255
10.2 Duality......Page 261
10.3 Euler’s Formula......Page 271
10.4 Bridges......Page 275
10.5 Kuratowski’s Theorem......Page 280
10.6 Surface Embeddings of Graphs......Page 287
10.7 Related Reading......Page 294
11.1 Colourings of Planar Maps......Page 299
11.2 The Five-Colour Theorem......Page 303
11.3 Related Reading......Page 305
12.1 Stable Sets......Page 307
12.2 Tur ́an’s Theorem......Page 313
12.3 Ramsey’s Theorem......Page 320
12.4 The Regularity Lemma......Page 329
12.5 Related Reading......Page 338
13.1 Random Graphs......Page 341
13.2 Expectation......Page 345
13.3 Variance......Page 354
13.4 Evolution of Random Graphs......Page 359
13.5 The Local Lemma......Page 362
13.6 Related Reading......Page 367
14.1 Chromatic Number......Page 369
14.2 Critical Graphs......Page 378
14.3 Girth and Chromatic Number......Page 382
14.4 Perfect Graphs......Page 385
14.5 List Colourings......Page 389
14.6 The Adjacency Polynomial......Page 392
14.7 The Chromatic Polynomial......Page 398
14.8 Related Reading......Page 401
15.1 Chromatic Numbers of Surfaces......Page 403
15.2 The Four-Colour Theorem......Page 407
15.3 List Colourings of Planar Graphs......Page 417
15.4 Hadwiger’s Conjecture......Page 419
15.5 Related Reading......Page 423
16.1 Maximum Matchings......Page 425
16.2 Matchings in Bipartite Graphs......Page 431
16.3 Matchings in Arbitrary Graphs......Page 438
16.4 Perfect Matchings and Factors......Page 442
16.5 Matching Algorithms......Page 449
16.6 Related Reading......Page 461
17.1 Edge Chromatic Number......Page 463
17.2 Vizing’s Theorem......Page 467
17.3 Snarks......Page 473
17.4 Coverings by Perfect Matchings......Page 476
17.5 List Edge Colourings......Page 478
17.6 Related Reading......Page 482
18.1 Hamiltonian and Nonhamiltonian Graphs......Page 483
18.2 Nonhamiltonian Planar Graphs......Page 490
18.3 Path and Cycle Exchanges......Page 495
18.4 Path Exchanges and Parity......Page 504
18.5 Hamilton Cycles in Random Graphs......Page 511
18.6 Related Reading......Page 513
19.1 Coverings and Packings in Hypergraphs......Page 515
19.2 Coverings by Directed Paths......Page 519
19.3 Coverings by Directed Cycles......Page 524
19.4 Packings of Branchings......Page 530
19.5 Packings of Directed Cycles and Directed Bonds......Page 532
19.6 Related Reading......Page 538
20.1 Circulations and Tensions......Page 539
20.2 Basis Matrices......Page 543
20.3 Feasible Circulations and Tensions......Page 546
20.4 The Matrix–Tree Theorem......Page 551
20.5 Resistive Electrical Networks......Page 554
20.6 Perfect Squares......Page 559
20.7 Random Walks on Graphs......Page 563
20.8 Related Reading......Page 568
21.1 Circulations and Colourings......Page 569
21.2 Integer Flows......Page 572
21.3 Tutte’s Flow Conjectures......Page 579
21.4 Edge-Disjoint Spanning Trees......Page 581
21.5 The Four-Flow and Eight-Flow Theorems......Page 585
21.6 The Six-Flow Theorem......Page 587
21.7 The Tutte Polynomial......Page 590
21.8 Related Reading......Page 594
Reconstruction......Page 595
Coverings, Decompositions, and Packings......Page 596
Embeddings......Page 597
Ramsey Numbers......Page 598
Vertex Colourings......Page 599
Edge Colourings......Page 600
Paths and Cycles in Digraphs......Page 601
Hamilton Paths and Cycles in Graphs......Page 602
Hypergraphs......Page 603
References......Page 605
General Mathematical Notation......Page 635
Graph Parameters......Page 637
Operations and Relations......Page 639
Families of Graphs......Page 641
Structures......Page 643
Other Notation......Page 645
Index......Page 649

Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics – computer science, combinatorial optimization, and operations research in particular – but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance.
The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises - of varying levels of difficulty - are provided to help the reader master the techniques and reinforce their grasp of the material.
A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters.
Visit the graph theory book blog at: http://blogs.springer.com/bondyandmurty/.

The Primary Aim Of This Book Is To Present A Coherent Introduction To The Subject, Suitable As A Textbook For Advanced Undergraduate And Beginning Graduate Students In Mathematics And Computer Science. It Provides A Systematic Treatment Of The Theory Of Graphs Without Sacrificing Its Intuitive And Aesthetic Appeal. Commonly Used Proof Techniques Are Described And Illustrated, And A Wealth Of Exercises - Of Varying Levels Of Difficulty - Are Provided To Help The Reader Master The Techniques And Reinforce Their Grasp Of The Material. A Second Objective Is To Serve As An Introduction To Research In Graph Theory. To This End, Sections On More Advanced Topics Are Included, And A Number Of Interesting And Challenging Open Problems Are Highlighted And Discussed In Some Detail. Despite This More Advanced Material, The Book Has Been Organized In Such A Way That An Introductory Course On Graph Theory Can Be Based On The First Few Sections Of Selected Chapters.--jacket. Graphs -- Subgraphs -- Connected Graphs -- Trees -- Separable And Nonseparable Graphs -- Tree-search Algorithms -- Flows In Networks -- Complexity Of Algorithms -- Connectivity -- Planar Graphs -- The Four-colour Problem -- Stable Sets And Cliques -- The Probabilistic Method -- Vertex Colourings -- Colourings Of Maps -- Matchings -- Edge Colourings -- Hamilton Cycles -- Coverings And Packings In Directed Graphs -- Electrical Networks -- Integer Flows And Coverings -- Unsolved Problems. J.a. Bondy And U.s.r. Murty. Includes Bibliographical References And Index.

"Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics--computer science, combinatorial optimization, and operations research in particular--but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance. The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises--of varying levels of difficulty--are provided to help the reader master the techniques and reinforce their grasp of the material. A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters"--Cover.

The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory.

2011-07-22