A textbook of graph theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2000
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 227 Seiten graph. Darst. |
| ISBN: | 0387988599 |
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Record in the Search Index
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| adam_text | Contents
Preface vii
I Basic Results 1
1.0 Introduction 1
1.1 Basic Concepts 2
1.2 Subgraphs 8
1.3 Degrees of Vertices 10
1.4 Paths and Connectedness 13
1.5 Automorphism of a Simple Graph 18
1.6 Line Graphs 20
1.7 Operations on Graphs 25
1.8 An Application to Chemistry 29
1.9 Miscellaneous Exercises 31
Notes 32
II Directed Graphs 33
2.0 Introduction 33
2.1 Basic Concepts 33
2.2 Tournaments 35
2.3 /t Partite Tournaments 38
Notes 43
III Connectivity 44
3.0 Introduction 44
3.1 Vertex Cuts and Edge Cuts 44
x Contents
3.2 Connectivity and Edge Connectivity 48
3.3 Blocks 54
3.4 Cyclical Edge Connectivity of a Graph 56
3.5 Menger s Theorem 57
3.6 Exercises 65
Notes 66
IV Trees 67
4.0 Introduction 67
4.1 Definition, Characterization, and Simple Properties 67
4.2 Centers and Centroids 72
4.3 Counting the Number of Spanning Trees 75
4.4 Cayley s Formula 79
4.5 Helly Property 80
4.6 Exercises 81
Notes 82
V Independent Sets and Matchings 83
5.0 Introduction 83
5.1 Vertex Independent Sets and Vertex Coverings 83
5.2 Edge Independent Sets 85
5.3 Matchings and Factors 87
5.4 Matchings in Bipartite Graphs 90
5.5* Perfect Matchings and the Tutte Matrix 99
Notes 101
VI Eulerian and Hamiltonian Graphs 102
6.0 Introduction 102
6.1 Eulerian Graphs 102
6.2 Hamiltonian Graphs 107
6.3* Pancyclic Graphs 115
6.4 Hamilton Cycles in Line Graphs 118
6.5 2 Factorable Graphs 124
6.6 Exercises 126
Notes 127
VII Graph Colorings 128
7.0 Introduction 128
7.1 Vertex Colorings 128
7.2 Critical Graphs 132
7.3 Triangle Free Graphs 136
7.4 Edge Colorings of Graphs 138
7.5 Snarks 144
7.6 Kirkman s Schoolgirls Problem 145
7.7 Chromatic Polynomials 147
Notes 150
Contents xi
VIII Planarity 152
8.0 Introduction 152
8.1 Planar and Nonplanar Graphs 152
8.2 Euler Formula and Its Consequences 157
8.3 K5 and K33 are Nonplanar Graphs 162
8.4 Dual of a Plane Graph 164
8.5 The Four Color Theorem and the Heawood
Five Color Theorem 167
8.6 Kuratowski s Theorem 170
8.7 Hamiltonian Plane Graphs 178
8.8 Tait Coloring 180
Notes 184
IX Triangulated Graphs 185
9.0 Introduction 185
9.1 Perfect Graphs 185
9.2 Triangulated Graphs 187
9.3 Interval Graphs 190
9.4 Bipartite Graph B(G) of a Graph G 192
9.5 Circular Arc Graphs 193
9.6 Exercises 193
9.7 Phasing of Traffic Lights at a Road Junction 195
Notes 198
X Applications 199
10.0 Introduction 199
10.1 The Connector Problem 199
10.2 Kruskal s Algorithm 200
10.3 Prim s Algorithm 202
10.4 Shortest Path Problems 203
10.5 Timetable Problem 205
10.6 Application to Social Psychology 207
10.7 Exercises 210
Notes 210
List of Symbols 213
References 217
Index 223
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:37:23Z |
| institution | BVB |
| isbn | 0387988599 |
| language | English |
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| physical | XI, 227 Seiten graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| spelling | Balakrishnan, Rangaswami Verfasser (DE-588)143438018 aut A textbook of graph theory R. Balakrishnan, K. Ranganathan New York, NY [u.a.] Springer 2000 XI, 227 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Graphentheorie Graph theory Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Ranganathan, K. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008853189&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Balakrishnan, Rangaswami Ranganathan, K. A textbook of graph theory Graphentheorie Graph theory Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 |
| title | A textbook of graph theory |
| title_auth | A textbook of graph theory |
| title_exact_search | A textbook of graph theory |
| title_full | A textbook of graph theory R. Balakrishnan, K. Ranganathan |
| title_fullStr | A textbook of graph theory R. Balakrishnan, K. Ranganathan |
| title_full_unstemmed | A textbook of graph theory R. Balakrishnan, K. Ranganathan |
| title_short | A textbook of graph theory |
| title_sort | a textbook of graph theory |
| topic | Graphentheorie Graph theory Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphentheorie Graph theory |
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