Topological theory of graphs:
This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2017]
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| Subjects: | |
| Online Access: | DE-1046 DE-573 DE-898 DE-859 DE-860 DE-91 DE-20 DE-706 DE-739 DE-1043 DE-858 Volltext |
| Summary: | This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of MacLane (on cycle bases), and of Whitney (on duality) for planarity. Relevant problems include the Jordan axiom in polyhedral forms, efficient methods for extremality and for recognizing a variety of embeddings (including rectilinear layouts in VLSI), and pan-polynomials, including those of Jones, Kauffman (on knots), and Tutte (on graphs), among others. Contents Preliminaries Polyhedra Surfaces Homology on Polyhedra Polyhedra on the Sphere Automorphisms of a Polyhedron Gauss Crossing Sequences Cohomology on Graphs Embeddability on Surfaces Embeddings on Sphere Orthogonality on Surfaces Net Embeddings Extremality on Surfaces Matroidal Graphicness Knot Polynomials |
| Physical Description: | 1 Online-Ressource (XII, 357 Seiten) |
| ISBN: | 9783110479492 |
| DOI: | 10.1515/9783110479492 |
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| isbn | 9783110479492 |
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| spelling | Liu, Yanpei 1939- Verfasser (DE-588)1132884713 aut Topological theory of graphs Yanpei Liu Berlin ; Boston De Gruyter [2017] © 2017 1 Online-Ressource (XII, 357 Seiten) txt rdacontent c rdamedia cr rdacarrier This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of MacLane (on cycle bases), and of Whitney (on duality) for planarity. Relevant problems include the Jordan axiom in polyhedral forms, efficient methods for extremality and for recognizing a variety of embeddings (including rectilinear layouts in VLSI), and pan-polynomials, including those of Jones, Kauffman (on knots), and Tutte (on graphs), among others. Contents Preliminaries Polyhedra Surfaces Homology on Polyhedra Polyhedra on the Sphere Automorphisms of a Polyhedron Gauss Crossing Sequences Cohomology on Graphs Embeddability on Surfaces Embeddings on Sphere Orthogonality on Surfaces Net Embeddings Extremality on Surfaces Matroidal Graphicness Knot Polynomials Graphentheorie (DE-588)4113782-6 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Topologie (DE-588)4060425-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-3-11-047669-9 Erscheint auch als epub 978-3-11-047922-5 https://doi.org/10.1515/9783110479492 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Liu, Yanpei 1939- Topological theory of graphs Graphentheorie (DE-588)4113782-6 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4060425-1 |
| title | Topological theory of graphs |
| title_auth | Topological theory of graphs |
| title_exact_search | Topological theory of graphs |
| title_full | Topological theory of graphs Yanpei Liu |
| title_fullStr | Topological theory of graphs Yanpei Liu |
| title_full_unstemmed | Topological theory of graphs Yanpei Liu |
| title_short | Topological theory of graphs |
| title_sort | topological theory of graphs |
| topic | Graphentheorie (DE-588)4113782-6 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Graphentheorie Topologie |
| url | https://doi.org/10.1515/9783110479492 |
| work_keys_str_mv | AT liuyanpei topologicaltheoryofgraphs |