Polytopes and Graphs (Hardcover) (ISBN-13: 9781009257817)

This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field.

Author: Guillermo Pineda Villavicencio
ISBN-10: 1009257811
ISBN-13: 9781009257817
Publisher: Cambridge University Press
Language: English
Published: 03/21/2024
Pages: 480
Format: Hardcover
Weight: 1.78lbs
Size: 9.00h x 6.00w x 1.06d