Convexity and Discrete Geometry Including Graph Theory: Mulhouse, France, September 2014

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Karim Adiprasito, Imre Bárány, Costin Vilcu
Springer, May 2, 2016 - Mathematics - 280 pages

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.

 

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Contents

From Convex to Magic
3
Transformations of Digraphs Viewed as Intersection Digraphs
27
Acute Triangulations of Rectangles with Angles Bounded Below
36
Multicompositions in Exponential Counting of Hypohamiltonian Snarks
47
Hamiltonicity in ktreeHalin Graphs
59
Reflections of Planar Convex Bodies
69
Steinhaus Conditions for Convex Polyhedra
77
About the Hausdorff Dimension of the Set of Endpoints of Convex Surfaces
85
Complex Conference Matrices Complex Hadamard Matrices and Complex Equiangular Tight Frames
181
Envelopes of αSections
192
Selected Open and Solved Problems in Computational Synthetic Geometry
219
Reductions of 3Connected Quadrangulations of the Sphere
231
Paths on the Sphere Without Small Angles
239
Seven Problems on Hypohamiltonian and Almost Hypohamiltonian Graphs
253
Six Problems on the Length of the Cut Locus
256
An Existence Problem for Matroidal Families
261

About a Surprising Computer Program of Matthias Müller
97
On the Connected Spanning Cubic Subgraph Problem
109
Extremal Results on Intersection Graphs of Boxes in mathbbRd
137
On the Helly Dimension of Hanner Polytopes
145
T4 Families of Disjoint Ovals
155
Fair Partitioning by Straight Lines
161
Fixed Point Theorems for Multivalued Zamfirescu Operators in Convex Kasahara Spaces
166
Two Problems on Cages for Discs
263
Cubical Pachner Moves
265
Problems in Discrete Geometry
269
What Is the Minimal Cardinal of a Family Which Shatters All dSubsets of a Finite Set?
274
Some Open Problems of Ramsey Minimal Graphs
279
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