The Foundations of Topological Graph Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1995
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced |
| Beschreibung: | 1 Online-Ressource (IX, 178p. 69 illus) |
| ISBN: | 9781461225409 9781461275732 |
| DOI: | 10.1007/978-1-4612-2540-9 |
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| 500 | |a This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced | ||
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Datensatz im Suchindex
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| author | Bonnington, C. Paul |
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| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2540-9 |
| format | Electronic eBook |
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| id | DE-604.BV042420040 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461225409 9781461275732 |
| language | English |
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| spelling | Bonnington, C. Paul Verfasser aut The Foundations of Topological Graph Theory by C. Paul Bonnington, Charles H. C. Little New York, NY Springer New York 1995 1 Online-Ressource (IX, 178p. 69 illus) txt rdacontent c rdamedia cr rdacarrier This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced Mathematics Combinatorics Mathematik Topologische Graphentheorie (DE-588)4341226-9 gnd rswk-swf Topologische Graphentheorie (DE-588)4341226-9 s 1\p DE-604 Little, Charles H. C. Sonstige oth https://doi.org/10.1007/978-1-4612-2540-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bonnington, C. Paul The Foundations of Topological Graph Theory Mathematics Combinatorics Mathematik 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 by C. Paul Bonnington, Charles H. C. Little |
| title_fullStr | The Foundations of Topological Graph Theory by C. Paul Bonnington, Charles H. C. Little |
| title_full_unstemmed | The Foundations of Topological Graph Theory by C. Paul Bonnington, Charles H. C. Little |
| title_short | The Foundations of Topological Graph Theory |
| title_sort | the foundations of topological graph theory |
| topic | Mathematics Combinatorics Mathematik Topologische Graphentheorie (DE-588)4341226-9 gnd |
| topic_facet | Mathematics Combinatorics Mathematik Topologische Graphentheorie |
| url | https://doi.org/10.1007/978-1-4612-2540-9 |
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