{"product_id":"polytopes-and-graphs-hardback-9781009257817","title":"Polytopes and Graphs (Hardback) 9781009257817","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003ePolytopes and Graphs\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAn introduction to convex polytopes and their graphs, including both background material and cutting-edge research.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eGuillermo Pineda Villavicencio (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009257817, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 March 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e480 pages\u003cbr\u003e23.5 x 15.8 x 3 cm, 0.84 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'… Villavicencio has produced a most welcome addition to the mathematical literature on polytopes. It is accessible and thorough, and it underscores developments from the past two decades: in other words, this book fills a gap within the existing set of texts. The book points the interested reader in numerous directions for further investigation and provides challenging exercises. … I highly recommend it to anyone wishing to explore the world of polytopes, especially students.' Robert Davis, Notices of the American Mathematical Society\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Introduction\u003cbr\u003e 2. Polytopes\u003cbr\u003e 3. Polytopal graphs\u003cbr\u003e 4. Connectivity\u003cbr\u003e 5. Reconstruction\u003cbr\u003e 6. Decomposition\u003cbr\u003e 7. Diameter\u003cbr\u003e 8. Faces\u003cbr\u003e A. Open problems\u003cbr\u003e B. Topology\u003cbr\u003e C. Graphs\u003cbr\u003e References\u003cbr\u003e Glossary\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52453593809176,"sku":"9781009257817","price":53.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009257817i.jpg?v=1785287352","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/polytopes-and-graphs-hardback-9781009257817","provider":"Freshly Printed Books","version":"1.0","type":"link"}