TY - BOOK ID - 145931192 TI - Polytopes and graphs PY - 2024 SN - 100925779X 1009257781 PB - Cambridge, United Kingdom ; New York, NY : Cambridge University Press, DB - UniCat KW - Convex polytopes KW - Convex polytopes. UR - https://www.unicat.be/uniCat?func=search&query=sysid:145931192 AB - 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. ER -