Polytopes and Graphs
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.
1144045963
Polytopes and Graphs
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.
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Polytopes and Graphs

Polytopes and Graphs

by Guillermo Pineda Villavicencio
Polytopes and Graphs

Polytopes and Graphs

by Guillermo Pineda Villavicencio

Overview

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.

Product Details

ISBN-13: 9781009257817
Publisher: Cambridge University Press
Publication date: 03/21/2024
Series: Cambridge Studies in Advanced Mathematics , #211
Pages: 480
Product dimensions: 6.22(w) x 9.25(h) x 1.18(d)

About the Author

Guillermo Pineda Villavicencio is an Associate Professor in Computer Science and Mathematics at Deakin University, Australia, and a Fellow of AdvanceHE. He conducts research on graph theory and discrete geometry, the construction and analysis of large networks, and applications of mathematics to health informatics. He is an Accredited Member of the Australian Mathematical Society and served on its Council from 2018 to 2022. He is also a Life Member of the Combinatorial Mathematics Society of Australasia.

Table of Contents

Preface; 1. Introduction; 2. Polytopes; 3. Polytopal graphs; 4. Connectivity; 5. Reconstruction; 6. Decomposition; 7. Diameter; 8. Faces; A. Open problems; B. Topology; C. Graphs; References; Glossary; Index.
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