Applied and algorithmic graph theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
McGraw-Hill
1993
|
| Series: | International series in pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 395 S. Ill., graph. Darst. |
| ISBN: | 0075571013 |
Staff View
MARC
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| 245 | 1 | 0 | |a Applied and algorithmic graph theory |c Gary Chartrand ; Ortrud R. Oellermann |
| 264 | 1 | |a New York u.a. |b McGraw-Hill |c 1993 | |
| 300 | |a XVII, 395 S. |b Ill., graph. Darst. | ||
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| 490 | 0 | |a International series in pure and applied mathematics | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface xv
1 An Introduction to Graphs l
1.1 What is a Graph? l
1.2 The Degree of a Vertex 5
1.3 Isomorphic Graphs 9
1.4 Subgraphs 12
1.5 Degree Sequences 15
1.6 Connected Graphs 20
1.7 Cut Vertices and Bridges 22
1.8 Special Graphs 25
1.9 Digraphs 31
2 An Introduction to Algorithms 38
2.1 Algorithmic Complexity 38
2.2 Search Algorithms 43
2.3 Sorting Algorithms 46
2.4 Introducing NP Completeness 49
2.5 Greedy Algorithms 54
2.6 Representing Graphs in a Computer 57
3 Trees 62
3.1 Properties of Trees 62
3.2 Rooted Trees 68
3.3 Depth First Search
3.4 Depth First Search: A Tool for Finding Blocks 74
3.5 Breadth First Search 79
3.6 The Minimum Spanning Tree Problem 85
4 Paths and Distance in Graphs 99
4.1 Distance in Graphs 99
4.2 Distance in Weighted Graphs 104
xi
Xii CONTENTS
4.3 The Center and Median of a Graph 111
4.4 Activity Digraphs and Critical Paths 117
4.5 Error Correcting Codes 123
5 Networks 129
5.1 An Introduction to Networks 129
5.2 The Max Flow Min Cut Theorem 136
5.3 A Max Flow Min Cut Algorithm 141
5.4 The Complexity of the Max Flow Min Cut Algorithm 144
5.5 Connectivity and Edge Connectivity 148
5.6 Menger s Theorem 152
6 Matchings and Factorizations 161
6.1 An Introduction to Matchings 161
6.2 Maximum Matchings in Bipartite Graphs 166
6.3 Maximum Matchings in General Graphs 178
6.4 Factorizations 186
6.5 Block Designs 198
7 Eulerian Graphs 205
7.1 An Introduction to Eulerian Graphs 205
7.2 Characterizing Eulerian Graphs Again 212
7.3 The Chinese Postman Problem 214
7.4 Eulerian Digraphs 218
8 Hamiltonian Graphs 226
8.1 An Introduction to Hamiltonian Graphs 226
8.2 Which Graphs are Hamiltonian? 229
8.3 The Traveling Salesman Problem 238
9 Planar Graphs 247
9.1 Properties of Planar Graphs 247
9.2 A Planarity Testing Algorithm 255
9.3 The Crossing Number and the Thickness of a Graph 266
9.4 The Genus of a Graph 271
9.5 Graph Minors 277
10 Coloring Graphs 283
10.1 Vertex Colorings 283
10.2 Chromatic Polynomials 296
10.3 Edge Colorings 300
10.4 The Four Color Problem 305
11 Digraphs 311
11.1 Strong Digraphs 311
11.2 Depth First Search in Digraphs 314
11.3 Strongly Connected Components 319
11.4 Tournaments 326
contents xiii
12 Extremal Graph Theory 333
12.1 Turin s Theorem 333
12.2 Ramsey Numbers 336
12.3 Generalized Ramsey Numbers 340
Hints and Solutions to Odd Numbered Exercises 345
Index 389
|
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| id | DE-604.BV007753765 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:08:54Z |
| institution | BVB |
| isbn | 0075571013 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005096678 |
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| owner_facet | DE-739 DE-91 DE-BY-TUM DE-703 DE-11 |
| physical | XVII, 395 S. Ill., graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | International series in pure and applied mathematics |
| spelling | Chartrand, Gary Verfasser aut Applied and algorithmic graph theory Gary Chartrand ; Ortrud R. Oellermann New York u.a. McGraw-Hill 1993 XVII, 395 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in pure and applied mathematics Teoria dos grafos larpcal Graph theory Graphentheorie (DE-588)4113782-6 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Algorithmus (DE-588)4001183-5 s Oellermann, Ortrud R. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005096678&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chartrand, Gary Oellermann, Ortrud R. Applied and algorithmic graph theory Teoria dos grafos larpcal Graph theory Graphentheorie (DE-588)4113782-6 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4001183-5 |
| title | Applied and algorithmic graph theory |
| title_auth | Applied and algorithmic graph theory |
| title_exact_search | Applied and algorithmic graph theory |
| title_full | Applied and algorithmic graph theory Gary Chartrand ; Ortrud R. Oellermann |
| title_fullStr | Applied and algorithmic graph theory Gary Chartrand ; Ortrud R. Oellermann |
| title_full_unstemmed | Applied and algorithmic graph theory Gary Chartrand ; Ortrud R. Oellermann |
| title_short | Applied and algorithmic graph theory |
| title_sort | applied and algorithmic graph theory |
| topic | Teoria dos grafos larpcal Graph theory Graphentheorie (DE-588)4113782-6 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Teoria dos grafos Graph theory Graphentheorie Algorithmus |
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