Includes overviews of evolving areas in convexity, discrete geometry and graph theory
Presents easily understandable, but surprising, properties, obtained using topological, geometric and graph theoretic tools
Written by experts from all over the word
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
Topics
Convex and Discrete Geometry
Graph Theory
Combinatorics
Global Analysis and Analysis on Manifolds
Author(s): Karim Alexander Adiprasito, Imre Bárány, Costin Vilcu (eds.)
Series: Springer Proceedings in Mathematics & Statistics 148
Edition: 1
Publisher: Springer
Year: 2016
Language: English
Pages: C,X,280
Tags: Convex and Discrete Geometry; Graph Theory; Combinatorics; Global Analysis and Analysis on Manifolds
Front Matter....Pages i-x
Front Matter....Pages 1-1
Tudor Zamfirescu: From Convex to Magic....Pages 3-25
Transformations of Digraphs Viewed as Intersection Digraphs....Pages 27-35
Acute Triangulations of Rectangles, with Angles Bounded Below....Pages 37-46
Multi-compositions in Exponential Counting of Hypohamiltonian Snarks....Pages 47-58
Hamiltonicity in k-tree-Halin Graphs....Pages 59-68
Reflections of Planar Convex Bodies....Pages 69-76
Steinhaus Conditions for Convex Polyhedra....Pages 77-84
About the Hausdorff Dimension of the Set of Endpoints of Convex Surfaces....Pages 85-95
About a Surprising Computer Program of Matthias Müller....Pages 97-108
On the Connected Spanning Cubic Subgraph Problem....Pages 109-136
On the Helly Dimension of Hanner Polytopes....Pages 137-144
Fair Partitioning by Straight Lines....Pages 145-154
Fixed Point Theorems for Multivalued Zamfirescu Operators in Convex Kasahara Spaces....Pages 155-160
Complex Conference Matrices, Complex Hadamard Matrices and Complex Equiangular Tight Frames....Pages 161-165
Selected Open and Solved Problems in Computational Synthetic Geometry....Pages 167-179
Reductions of 3-Connected Quadrangulations of the Sphere....Pages 181-191
Paths on the Sphere Without Small Angles....Pages 193-218
Front Matter....Pages 219-229
Seven Problems on Hypohamiltonian and Almost Hypohamiltonian Graphs....Pages 231-238
Six Problems on the Length of the Cut Locus....Pages 239-249
An Existence Problem for Matroidal Families....Pages 251-251
Two Problems on Cages for Discs....Pages 253-255
Problem Session: Cubical Pachner Moves....Pages 257-259
Problems in Discrete Geometry....Pages 261-262
What Is the Minimal Cardinal of a Family Which Shatters All d-Subsets of a Finite Set?....Pages 263-264
Some Open Problems of Ramsey Minimal Graphs....Pages 265-268
....Pages 269-273
