| Topological Theory of Graphs Contributor(s): Liu, Yanpei (Author), University of Science &. Technology (Contribution by) |
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ISBN: 311047669X ISBN-13: 9783110476699 Publisher: de Gruyter OUR PRICE: $179.54 Product Type: Hardcover - Other Formats Published: March 2017 |
| Additional Information |
| BISAC Categories: - Mathematics | Discrete Mathematics - Mathematics | Topology - General - Mathematics | Geometry - General |
| Physical Information: 1" H x 6.9" W x 9.6" (1.90 lbs) 369 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 |