Topological Theory of Graphs / Yanpei Liu

By:

Liu, Yanpei, 1939- [VerfasserIn]

9783110479492
9783110479225
9783110479508

Subject(s):

Additional physical formats: 9783110479508. | 9783110476699 | Erscheint auch als: Topological theory of graphs. Druck-Ausgabe Berlin : De Gruyter, 2017. XI, 357 Seiten | Erscheint auch als: 978-3-11-047669-9 Druck-Ausgabe | Erscheint auch als: 978-3-11-047922-5 Druck-Ausgabe | Erscheint auch als: 978-3-11-047950-8 Druck-AusgabeDDC classification:

511/.5 23

MSC: MSC: *05-02 | 05C10 | 52B05RVK: RVK: SK 890Local classification: Lokale Notation: math 9.3 | math 5.0LOC classification:

QA166.195
QA166

DOI: DOI: 10.1515/9783110479492Online resources:

Zugang im Netz des KIT

Contents:

Frontmatter -- -- Preface to DG Edition -- -- Preface to USTC Edition -- -- Contents -- -- 1. Preliminaries -- -- 2. Polyhedra -- -- 3. Surfaces -- -- 4. Homology on Polyhedra -- -- 5. Polyhedra on the Sphere -- -- 6. Automorphisms of a Polyhedron -- -- 7. Gauss Crossing Sequences -- -- 8. Cohomology on Graphs -- -- 9. Embeddability on Surfaces -- -- 10. Embeddings on Sphere -- -- 11. Orthogonality on Surfaces -- -- 12. Net Embeddings -- -- 13. Extremality on Surfaces -- -- 14. Matroidal Graphicness -- -- 15. Knot Polynomials -- -- Bibliography -- -- Subject Index -- -- Author Index

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 PolynomialsPPN: PPN: 882894307Package identifier: Produktsigel: EBA-BACKALL | EBA-CL-MTPY | EBA-DGALL | EBA-EBACKALL | EBA-EBKALL | EBA-ECL-MTPY | EBA-EEBKALL | EBA-ESTMALL | EBA-STMALL | GBV-23-DGG-HSU | GBV-deGruyter-alles | ZDB-23-DGG | ZDB-23-DMA

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In English