Bounded degree spanning trees:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paderborn
1997
|
| Schriftenreihe: | Heinz-Nixdorf-Institut <Paderborn>: HNI-Verlagsschriftenreihe
35 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Paderborn, Univ.-GH, Diss., 1997 |
| Beschreibung: | IX, 139 S. Ill., graph. Darst. |
| ISBN: | 3931466345 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Previous Work 4
1.2 New Results 4
1.3 Organization 8
2 Basic Definitions 11
2.1 Graphs 11
2.2 Topology 12
2.3 Embedding 16
2.3.1 Planar Embedding 18
3 Decremental Biconnectivity in Planar Graphs 21
3.1 Preliminaries 23
3.2 Data Structures for Biconnectivity 24
3.3 Maintaining the Data Structure During an Edge Deletion 27
3.4 Additional Operations 30
I Algorithms for Bounded Degree Spanning Trees 35
4 A7 Spanning Trees in 2 Connected Graphs 37
4.1 A^ Spanning Trees in Well Structured Graphs 38
4.1.1 Assertions 40
4.1.2 Data Structure and Operations for the Graph 40
4.1.3 Data Structure and Operations for the Auxiliary Graph .... 41
4.1.4 Data Structure and Operations for the Forest 41
4.1.5 Split Operations in the Graph 42
4.1.6 Recursive Algorithm 50
4.1.7 Analysis of the Running Time 55
4.2 Biconnected Graphs 57
5 A7 Spanning Trees in 2 Connected Planar Graphs 59
vii
viii CONTENTS
6 3 Spanning Trees in 3 Connected Planar Graphs 63
6.1 Basic Definitions 63
6.2 Basic Results and Barnette s Proof 64
6.3 Preliminaries 66
6.3.1 Data Structures 68
6.3.2 Assertions 69
6.3.3 Fast Queries 70
6.3.4 Deleting a Spare Edge 71
6.4 Algorithm 74
6.4.1 Trivial Edges 74
6.4.2 Running Time Analysis 76
6.5 Extensions 77
6.5.1 Planar Graphs 77
6.5.2 Projective Planar Graphs 78
7 Ar Spanning Trees in ^ Connected Graphs 83
7.1 Toughness 84
7.2 FR Algorithm 84
7.3 Adaption 86
7.4 Comparison: FR Versus A7 spanning trees 87
II 9iTC Results for Bounded Degree Spanning Trees 91
8 AT Spanning Trees in fc Connected Graphs 93
8.1 Hamiltonian Cycle Problem 93
8.1.1 Definitions 94
8.1.2 General Facts 94
8.1.3 Construction of Garey, Johnson and Tarjan 95
8.1.4 ^ Completeness Result for k ^ 5 101
8.1.5 A Special Perfect Matching 104
8.1.6 ^ Completeness Result 106
8.2 Hamiltonian Paths and Ap Spanning Trees in fc Connected Graphs of
Maximum Degree k(Ar 1) 108
8.2.1 Construction 109
8.2.2 ^ Completeness Result 110
8.3 Extensions and Remarks 113
9 Ar Spanning Trees in 2 Connected Planar Graphs 115
9.1 Preliminaries 116
9.2 Construction 117
9.3 Extensions to Other Surfaces 118
ix
10 Extensions to Other Surfaces 121
10.1 Projective Plane 121
10.2 Torus and Klein Bottle 121
11 Summary and Open Problems 125
11.1 Summary 125
11.2 Open Problems 125
A Basic Graph Definitions 129
Bibliography 133
|
| any_adam_object | 1 |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV011790788 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:15:49Z |
| institution | BVB |
| isbn | 3931466345 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007959737 |
| oclc_num | 75850080 |
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| owner | DE-355 DE-BY-UBR DE-91 DE-BY-TUM |
| owner_facet | DE-355 DE-BY-UBR DE-91 DE-BY-TUM |
| physical | IX, 139 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
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| series | Heinz-Nixdorf-Institut <Paderborn>: HNI-Verlagsschriftenreihe |
| series2 | Heinz-Nixdorf-Institut <Paderborn>: HNI-Verlagsschriftenreihe |
| spelling | Strothmann, Willy-B. 1965- Verfasser (DE-588)120251639 aut Bounded degree spanning trees Willy-B. Strothmann Paderborn 1997 IX, 139 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Heinz-Nixdorf-Institut <Paderborn>: HNI-Verlagsschriftenreihe 35 Zugl.: Paderborn, Univ.-GH, Diss., 1997 Baum (DE-588)4004845-7 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Maximaler Baum (DE-588)4228499-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Baum (DE-588)4004845-7 s Graphentheorie (DE-588)4113782-6 s DE-604 Maximaler Baum (DE-588)4228499-5 s Heinz-Nixdorf-Institut <Paderborn>: HNI-Verlagsschriftenreihe 35 (DE-604)BV010410690 35 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007959737&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strothmann, Willy-B. 1965- Bounded degree spanning trees Heinz-Nixdorf-Institut <Paderborn>: HNI-Verlagsschriftenreihe Baum (DE-588)4004845-7 gnd Graphentheorie (DE-588)4113782-6 gnd Maximaler Baum (DE-588)4228499-5 gnd |
| subject_GND | (DE-588)4004845-7 (DE-588)4113782-6 (DE-588)4228499-5 (DE-588)4113937-9 |
| title | Bounded degree spanning trees |
| title_auth | Bounded degree spanning trees |
| title_exact_search | Bounded degree spanning trees |
| title_full | Bounded degree spanning trees Willy-B. Strothmann |
| title_fullStr | Bounded degree spanning trees Willy-B. Strothmann |
| title_full_unstemmed | Bounded degree spanning trees Willy-B. Strothmann |
| title_short | Bounded degree spanning trees |
| title_sort | bounded degree spanning trees |
| topic | Baum (DE-588)4004845-7 gnd Graphentheorie (DE-588)4113782-6 gnd Maximaler Baum (DE-588)4228499-5 gnd |
| topic_facet | Baum Graphentheorie Maximaler Baum Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007959737&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010410690 |
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