Name: Topological Theory of Graphs (en Inglés)
SKU: 51836897
Price: 165.83 USD
Availability: InStock
Author: Yanpei Liu

portada Topological Theory of Graphs (en Inglés)

Topological Theory of Graphs (en Inglés)

Formato

Libro Físico

Editorial

De Gruyter

Autor

Yanpei Liu

Año

2017

Idioma

Inglés

N° páginas

369

Encuadernación

Tapa Dura

ISBN13

9783110476699

Categorías

Matemáticas discretas

Topological Theory of Graphs (en Inglés)

Yanpei Liu (Autor) · De Gruyter · Tapa Dura

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Reseña del libro "Topological Theory of Graphs (en Inglés)"

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