Polytopes and Graphs

Released on by Guillermo Pineda Villavicencio
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  • Polytopes and Graphs Book Detail

  • Author : Guillermo Pineda Villavicencio
  • Release Date : 2024-02-29
  • Publisher : Cambridge University Press
  • Genre : Mathematics
  • Pages : 482
  • ISBN 13 : 1009257781
  • File Size : 30,30 MB
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Polytopes and Graphs by Guillermo Pineda Villavicencio PDF Summary

Book Description: 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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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

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Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The str

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Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions