Guillermo Pineda-Villavicencio

Polytopes and graphs

Polytopes and graphs

This page is dedicated to my book  Polytopes and Graphs. This material has been published by Cambridge University Press as ‘Polytopes and Graphs’ by Guillermo Pineda Villavicencio. A pre-publication copy of the book is available for personal use only from Deakin Research Online. This version is free to view and download for personal use only. It is not for redistribution, resale, or use in derivative works. © Guillermo Pineda Villavicencio 2018-2024.

‘Polytopes and Graphs’ places graphs at the heart of the study of polytopes. It covers topics on the graphs of polytopes and explores how these graphs elucidate aspects of the combinatorial structure of polytopes. The book seeks to concretely address two key questions:

  1. Given the graph of a polytope, what properties can we infer about the polytope?
  2. Given a class of polytopes, what properties characterise their graphs?
Updates on the open problems in the book

As of now, there are no new developments to report.