Matroid decomposition:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Academic Press
1992
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 398 S. zahlr. graph. Darst. |
| ISBN: | 0127012257 |
Internformat
MARC
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| 100 | 1 | |a Truemper, Klaus |e Verfasser |4 aut | |
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| 264 | 1 | |a Boston u.a. |b Academic Press |c 1992 | |
| 300 | |a X, 398 S. |b zahlr. graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804122583328620544 |
|---|---|
| adam_text | Contents
Preface ix
Chapter 1 Introduction 1
1.1 Summary 1
1.2 Historical Notes 3
Chapter 2 Basic Definitions 5
2.1 Overview and Notation 5
2.2 Graph Definitions 6
2.3 Matrix Definitions 18
2.4 Complexity of Algorithms 24
2.5 References 25
Chapter 3 From Graphs to Matroids 26
3.1 Overview 26
3.2 Graphs Produce Graphic Matroids 27
3.3 Binary Matroids Generalize Graphic Matroids 52
3.4 Abstract Matrices Produce All Matroids 71
3.5 Characterization of Binary Matroids 85
3.6 References 87
V
vi Contents
Chapter 4 Series Parallel and Delta Wye
Constructions 89
4.1 Overview 89
4.2 Series Parallel Construction 90
4.3 Delta Wye Construction for Graphs 96
4.4 Delta Wye Construction for Binary Matroids 101
4.5 Applications, Extensions, and References 109
Chapter 5 Path Shortening Technique Ill
5.1 Overview 111
5.2 Shortening of Paths 112
5.3 Intersection and Partitioning of Matroids 119
5.4 Extensions and References 125
Chapter 6 Separation Algorithm 128
6.1 Overview 128
6.2 Separation Algorithm 129
6.3 Sufficient Conditions for Induced Separations 134
6.4 Extensions of 3 Connected Minors 147
6.5 Extensions and References 150
Chapter 7 Splitter Theorem and Sequences of
Nested Minors 151
7.1 Overview 151
7.2 Splitter Theorem 152
7.3 Sequences of Nested Minors and
Wheel Theorem 157
7.4 Characterization of Planar Graphs 163
7.5 Extensions and References 165
Chapter 8 Matroid Sums 168
8.1 Overview 168
8.2 1 and 2 Sums 169
8.3 General fc Sums 173
8.4 Finding 1 , 2 , and 3 Sums 180
8.5 Delta Sum and Wye Sum 182
8.6 Extensions and References 186
Contents vii
Chapter 9 Matrix Total Unimodularity and
Matroid Regularity 188
9.1 Overview 188
9.2 Basic Results and Applications of
Total Unimodularity 189
9.3 Characterization of Regular Matroids 196
9.4 Characterization of Ternary Matroids 199
9.5 Extensions and References 202
Chapter 10 Graphic Matroids 205
10.1 Overview 205
10.2 Characterization of Planar Matroids 206
10.3 Regular Matroids with M{K3i3) Minors 214
10.4 Characterization of Graphic Matroids 224
10.5 Decomposition Theorems for Graphs 227
10.6 Testing Graphicness of Binary Matroids 238
10.7 Applications, Extensions, and References 241
Chapter 11 Regular Matroids 245
11.1 Overview 245
11.2 1 , 2 , and 3 Sum Compositions
Preserve Regularity 246
11.3 Regular Matroid Decomposition Theorem 251
11.4 Testing Matroid Regularity and
Matrix Total Unimodularity 259
11.5 Applications of Regular Matroid
Decomposition Theorem 260
11.6 Extensions and References 270
Chapter 12 Almost Regular Matroids 272
12.1 Overview 272
12.2 Characterization of Alpha Balanced Graphs 274
12.3 Several Matrix Classes 284
12.4 Definition and Construction of
Almost Regular Matroids 294
12.5 Matrix Constructions 302
12.6 Applications, Extensions, and References 312
viii Contents
Chapter 13 Max Flow Min Cut Matroids 314
13.1 Overview 314
13.2 2 Sum and Delta Sum Decompositions 316
13.3 Characterization of Max Flow Min Cut Matroids 326
13.4 Construction of Max Flow Min Cut Matroids and
Polynomial Algorithms 335
13.5 Graphs without Odd i^ Minors 340
13.6 Applications, Extensions, and References 348
References 350
Author Index 378
Subject Index 383
|
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:16:11Z |
| institution | BVB |
| isbn | 0127012257 |
| language | English |
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| physical | X, 398 S. zahlr. graph. Darst. |
| publishDate | 1992 |
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| publisher | Academic Press |
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| spelling | Truemper, Klaus Verfasser aut Matroid decomposition K. Truemper Boston u.a. Academic Press 1992 X, 398 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ungarn Strafverfahrensgesetz (DE-588)4138428-3 gnd rswk-swf Décomposition (Mathématiques) Décomposition (mathématiques) ram Matroïde Matroïdes Decomposition (Mathematics) Matroids Politische Meinungsäußerung (DE-588)4175032-9 gnd rswk-swf Zerlegung Mathematik (DE-588)4190746-2 gnd rswk-swf Matroid (DE-588)4128705-8 gnd rswk-swf Dekomposition (DE-588)4149030-7 gnd rswk-swf Matroid (DE-588)4128705-8 s Dekomposition (DE-588)4149030-7 s DE-604 Zerlegung Mathematik (DE-588)4190746-2 s DE-188 Ungarn Strafverfahrensgesetz (DE-588)4138428-3 u Politische Meinungsäußerung (DE-588)4175032-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005410564&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Truemper, Klaus Matroid decomposition Ungarn Strafverfahrensgesetz (DE-588)4138428-3 gnd Décomposition (Mathématiques) Décomposition (mathématiques) ram Matroïde Matroïdes Decomposition (Mathematics) Matroids Politische Meinungsäußerung (DE-588)4175032-9 gnd Zerlegung Mathematik (DE-588)4190746-2 gnd Matroid (DE-588)4128705-8 gnd Dekomposition (DE-588)4149030-7 gnd |
| subject_GND | (DE-588)4138428-3 (DE-588)4175032-9 (DE-588)4190746-2 (DE-588)4128705-8 (DE-588)4149030-7 |
| title | Matroid decomposition |
| title_auth | Matroid decomposition |
| title_exact_search | Matroid decomposition |
| title_full | Matroid decomposition K. Truemper |
| title_fullStr | Matroid decomposition K. Truemper |
| title_full_unstemmed | Matroid decomposition K. Truemper |
| title_short | Matroid decomposition |
| title_sort | matroid decomposition |
| topic | Ungarn Strafverfahrensgesetz (DE-588)4138428-3 gnd Décomposition (Mathématiques) Décomposition (mathématiques) ram Matroïde Matroïdes Decomposition (Mathematics) Matroids Politische Meinungsäußerung (DE-588)4175032-9 gnd Zerlegung Mathematik (DE-588)4190746-2 gnd Matroid (DE-588)4128705-8 gnd Dekomposition (DE-588)4149030-7 gnd |
| topic_facet | Ungarn Strafverfahrensgesetz Décomposition (Mathématiques) Décomposition (mathématiques) Matroïde Matroïdes Decomposition (Mathematics) Matroids Politische Meinungsäußerung Zerlegung Mathematik Matroid Dekomposition |
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