The foundations of topological graph theory
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
1995
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Bonnington, C. Paul |e Verfasser |0 (DE-588)172897637 |4 aut | |
| 245 | 1 | 0 | |a The foundations of topological graph theory |c C. Paul Bonnington, Charles H. C. Little |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 1995 | |
| 300 | |a IX, 178 Seiten |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverzeichnis Seiten 161 - 163 | ||
| 650 | 0 | 7 | |a Topologische Graphentheorie |0 (DE-588)4341226-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Topologische Graphentheorie |0 (DE-588)4341226-9 |D s |
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| 700 | 1 | |a Little, Charles H. C. |d 1947- |e Verfasser |0 (DE-588)172504279 |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006990270 | |
Datensatz im Suchindex
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| DE-BY-TUM_location | Mag |
| DE-BY-TUM_media_number | 040001046059 |
| _version_ | 1820815247232991232 |
| adam_text | Contents
Preface v
1 Introduction 1
1.1 Sets 1
1.2 Graphs 3
1.3 Subgraphs 4
1.4 Cocycles 4
1.5 Forests, trees, circuits, and paths 5
1.6 Some elementary results 5
1.7 Theorems about trees 9
1.8 Spanning trees 11
1.9 Eulerian graphs 12
1.10 Bipartite graphs 12
1.11 Contractions 13
1.12 Menger s theorem and n connected graphs 14
1.13 2 connected graphs 17
1.14 Blocks 17
1.15 The cycle and cocycle spaces of a graph 18
1.16 Double covers 20
2 Maps 23
2.1 Permutations 23
2.2 Maps 24
2.3 Imbeddings of maps 25
viii Contents
2.4 3 graphs 30
2.5 From maps to gems and back again 32
2.6 Premaps 35
3 Classification of Surfaces 39
3.1 Dipoles 40
3.2 Reduced and unitary 3 graphs 42
3.3 Canonical gems 48
3.4 Planar graphs 50
4 Consistent and Coherent Orientations 53
4.1 Orientations 53
4.2 Pairwise coherently orientable nets 56
4.3 Families of circuits 57
4.4 Rings 61
5 Non separating Curves in Surfaces 63
5.1 The main results and their topological implications 63
5.2 Permutation pairs 69
5.3 A condition for a b cycle to separate 75
5.4 Fundamental sets of semicycles 78
6 Mac Lane s Theorem for 3 Graphs 83
6.1 Congruence 83
6.2 Semicycle covers 84
6.3 Boundary covers 86
6.4 Partial congruence 89
6.5 Mac Lane s theorem 94
6.6 Whitney s characterisation 95
7 Kuratowski s Theorem 97
7.1 Corollaries of Mac Lane s theorem 97
7.2 Kuratowski s theorem 101
7.3 Wagner s theorem 106
8 Duality 111
8.1 Duals Ill
8.2 Constructing orthogonal graphs 114
8.3 Duality for planar graphs 115
8.4 The zigzag space 119
8.5 The principal edge tripartition for planar graphs 122
8.6 Walks 126
8.7 Principal cycles and principal cocycles 128
8.8 Diagonals 130
8.9 Every planar graph has a diagonal 132
8.10 No non planar graph has a diagonal 134
Contents ix
9 Rings of Bonds 143
9.1 Chordal graphs 143
9.2 Rings of bonds 144
10 Bridges 153
10.1 Residues and bridges 153
10.2 Tutte s characterisation 158
Bibliography 161
List of Symbols 165
Index 171
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| any_adam_object | 1 |
| author | Bonnington, C. Paul Little, Charles H. C. 1947- |
| author_GND | (DE-588)172897637 (DE-588)172504279 |
| author_facet | Bonnington, C. Paul Little, Charles H. C. 1947- |
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| author_sort | Bonnington, C. Paul |
| author_variant | c p b cp cpb c h c l chc chcl |
| building | Verbundindex |
| bvnumber | BV010491040 |
| classification_rvk | SK 280 SK 890 |
| classification_tum | MAT 057f |
| ctrlnum | (OCoLC)246773756 (DE-599)BVBBV010491040 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010491040 |
| illustrated | Illustrated |
| indexdate | 2025-01-08T13:51:13Z |
| institution | BVB |
| isbn | 0387945571 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006990270 |
| oclc_num | 246773756 |
| open_access_boolean | |
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| owner_facet | DE-20 DE-824 DE-91 DE-BY-TUM DE-739 DE-703 DE-12 DE-634 DE-83 DE-11 DE-188 DE-29T |
| physical | IX, 178 Seiten zahlr. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Bonnington, C. Paul Little, Charles H. C. 1947- The foundations of topological graph theory Topologische Graphentheorie (DE-588)4341226-9 gnd |
| subject_GND | (DE-588)4341226-9 |
| title | The foundations of topological graph theory |
| title_auth | The foundations of topological graph theory |
| title_exact_search | The foundations of topological graph theory |
| title_full | The foundations of topological graph theory C. Paul Bonnington, Charles H. C. Little |
| title_fullStr | The foundations of topological graph theory C. Paul Bonnington, Charles H. C. Little |
| title_full_unstemmed | The foundations of topological graph theory C. Paul Bonnington, Charles H. C. Little |
| title_short | The foundations of topological graph theory |
| title_sort | the foundations of topological graph theory |
| topic | Topologische Graphentheorie (DE-588)4341226-9 gnd |
| topic_facet | Topologische Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006990270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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