Cycle bases of graphs and spanning trees with many leaves: complexity results on planar and regular graphs
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | German |
| Veröffentlicht: |
2014
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| Schlagworte: | |
| Online-Zugang: | kostenfrei kostenfrei Inhaltsverzeichnis |
| Beschreibung: | 158 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Reich, Alexander |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Cycle bases of graphs and spanning trees with many leaves |b complexity results on planar and regular graphs |c vorgelegt von Alexander Reich |
| 264 | 1 | |c 2014 | |
| 300 | |a 158 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Cottbus-Senftenberg, Techn. Univ., Diss., 2014 | ||
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| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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Datensatz im Suchindex
| _version_ | 1804152180714766336 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION 11
1 PRELIMINARIES 15
1.1 GRAPH THEORY 15
1.2 CYCLES AND CYCLE SPACES 18
1.3 COMPLEXITY AND APPROXIMATION 22
2 SPANNING TREES WITH MANY LEAVES 29
2.1 INTRODUCTION 29
2.2 APPLICATIONS 31
2.3 AA P-COMPLETENESS
OF THE MLST
ON PLANAR CUBIC GRAPHS 33
2.3.1 CONNECTION OF THE 3-SETS 34
2.3.2 THE PROBLEMS 35
2.3.3 THE TRANSFORMATION 35
2.3.4 RESTRICTION TO BICONNECTED GRAPHS 39
2.4 AVX-COMPLETENESS OF THE MLST
ON REGULAR GRAPHS 41
2.4.1 THE PROBLEMS 41
2.4.2 THE TRANSFORMATION 42
2.4.3 EXTENSION TO GRAPHS WITH ARBITRARY ODD REGULARITY 45
2.5 ALGORITHMS FOR SELECTED GRAPH CLASSES 48
2.6 CONCLUSIONS AND OUTLOOKS 49
7
HTTP://D-NB.INFO/1052155413
8 CONTENTS
3 STRICTLY FUNDAMENTAL CYCLE BASES 51
3.1 INTRODUCTION 52
3.2 APPLICATIONS 53
3.3 BASIC DEFINITIONS AND PROPERTIES ON SFCBS 55
3.4 SFCBS ON PLANAR GRAPHS 59
3.4.1 DEFINITIONS FOR PLANAR GRAPHS 59
3.4.2 SFCBS ON WEIGHTED PLANAR GRAPHS 61
3.4.3 RELATIONSHIP TO THE OCST
PROBLEM 63
3.4.4 SFCBS ON NON-METRIC PLANAR GRAPHS 65
3.5
./VP-COMPLETENESS
OF
THE
MSFCB
IN PLANAR GRAPHS 68
3.5.1 THE PROBLEMS 68
3.5.2 THE TRANSFORMATION 69
3.6 OUTERPLANAR GRAPHS 81
3.6.1 INTRODUCTION 81
3.6.2 DEFINITION AND PROPERTIES ON OUTERPLANAR GRAPHS 82
3.6.3 MINOR MONOTONICITY 84
3.7 CYCLE ROOT GRAPHS 89
3.8 CONCLUSIONS 92
4 CLASSIFICATION OF ROBUST CYCLE BASES 93
4.1 INTRODUCTION 93
4.2 APPLICATIONS 94
4.3 CLASSES OF ROBUST CYCLE BASES 96
4.4 EXAMPLES OF ROBUST CYCLE BASES 97
4.5 RELATIONSHIP WITH FUNDAMENTAL BASES 104
4.6 CONCLUSIONS 112
CONTENTS 9
5 FURTHER CLASSES OF CYCLE BASES 113
5.1 P-BASES 114
5.1.1 DEFINITION OF P-BASES FOR DIRECTED AND UNDIRECTED GRAPHS 114
5.1.2 P-BASES FOR LARGE P 115
5.1.3 P-BASES FOR SMALL P 118
5.1.4 CONCLUSIONS 120
5.2 TOTALLY UNIMODULAR CYCLE BASES 120
5.2.1 INTRODUCTION 120
5.2.2 BASIC DEFINITIONS AND PROPERTIES ON TUM CYCLE BASES 121
5.2.3 TUM BASES VS. WEAKLY FUNDAMENTAL CYCLE BASES 124
5.2.4 CONCLUSIONS 132
5.3 INTEGRAL CYCLE BASES 133
5.3.1 INTRODUCTION 133
5.3.2 THE
PESP
FOR MODELING PERIODIC TIMETABLES 134
5.3.3 DEFINITION 136
5.3.4 AN INTEGRAL CYCLE BASIS WITHOUT SIMPLE CYCLES 137
5.3.5 TUM BASES AND THE EXCHANGE PROPERTY 138
5.3.6 CONCLUSIONS 140
BIBLIOGRAPHY 143
INDEX 153
LIST OF PROBLEMS 157
|
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| indexdate | 2024-07-10T01:06:37Z |
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| spelling | Reich, Alexander Verfasser aut Cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs vorgelegt von Alexander Reich 2014 158 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cottbus-Senftenberg, Techn. Univ., Diss., 2014 Zyklenraum (DE-588)4630853-2 gnd rswk-swf Planarer Graph (DE-588)4174783-5 gnd rswk-swf NP-vollständiges Problem (DE-588)4138229-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Planarer Graph (DE-588)4174783-5 s Zyklenraum (DE-588)4630853-2 s NP-vollständiges Problem (DE-588)4138229-8 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:kobv:co1-opus-30692 https://nbn-resolving.org/urn:nbn:de:kobv:co1-opus-30692 kostenfrei Volltext http://opus.kobv.de/btu/volltexte/2014/3069/ kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027284309&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reich, Alexander Cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs Zyklenraum (DE-588)4630853-2 gnd Planarer Graph (DE-588)4174783-5 gnd NP-vollständiges Problem (DE-588)4138229-8 gnd |
| subject_GND | (DE-588)4630853-2 (DE-588)4174783-5 (DE-588)4138229-8 (DE-588)4113937-9 |
| title | Cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs |
| title_auth | Cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs |
| title_exact_search | Cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs |
| title_full | Cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs vorgelegt von Alexander Reich |
| title_fullStr | Cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs vorgelegt von Alexander Reich |
| title_full_unstemmed | Cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs vorgelegt von Alexander Reich |
| title_short | Cycle bases of graphs and spanning trees with many leaves |
| title_sort | cycle bases of graphs and spanning trees with many leaves complexity results on planar and regular graphs |
| title_sub | complexity results on planar and regular graphs |
| topic | Zyklenraum (DE-588)4630853-2 gnd Planarer Graph (DE-588)4174783-5 gnd NP-vollständiges Problem (DE-588)4138229-8 gnd |
| topic_facet | Zyklenraum Planarer Graph NP-vollständiges Problem Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:kobv:co1-opus-30692 http://opus.kobv.de/btu/volltexte/2014/3069/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027284309&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT reichalexander cyclebasesofgraphsandspanningtreeswithmanyleavescomplexityresultsonplanarandregulargraphs |