Convexity and Discrete Geometry Including Graph Theory : Mulhouse, France, September 2014 / edited by Karim Adiprasito, Imre Bárány, Costin Vilcu.

Format:

Book

Contributor:

Adiprasito, Karim., Editor.

Bárány, Imre, Editor.

Vilcu, Costin., Editor.

Series:

Springer Proceedings in Mathematics & Statistics, 2194-1017 ; 148

Language:

English

Subjects (All):

Convex geometry.

Discrete geometry.

Graph theory.

Discrete mathematics.

Global analysis (Mathematics).

Manifolds (Mathematics).

Convex and Discrete Geometry.

Graph Theory.

Discrete Mathematics.

Global Analysis and Analysis on Manifolds.

Local Subjects:

Convex and Discrete Geometry.

Graph Theory.

Discrete Mathematics.

Global Analysis and Analysis on Manifolds.

Physical Description:

1 online resource (X, 280 p. 93 illus., 39 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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.

Contents:

Introduction

PART I Research Articles. Marcus: Tudor Zamfirescu: from convex to magic

Yuan: Acute Triangulations of Rectangles, with Angles Bounded Below

Skupien: Multi-compositions in exponential counting of hypohamiltonian snarks

Shabbir & T. Zamfirescu: Hamiltonicity in k-tree-Halin graphs

Schneider: Reflections of planar convex bodies

Rouyer: Steinhaus conditions for convex polyhedra

Riviere: About the Hausdorff dimension of the set of endpoints of convex surfaces

Prunescu: About a surprising computer program of Matthias Müller

Oliveros, Martinez & Montejano: Extremal results on intersection graphs of boxes in R^d

Massé, Euler & Lemarchand: On the connected spanning cubic subgraph problem

Kincses: On the Helly dimension of Hanner polytopes

Itoh & Ohtsuka: Classification of normal 2-polyhedra of positive constant curvature

Heppes& Jeronimo-Castro: T(4) families ofϕ-disjoint ovals

Fruchard & Magazinov: Fair partitioning by straight lines

Filip & Petrusel: Fixed point theorems for multivalued Zamfrescu operators in convex Kasahara spaces

Et-Taoui: Complex conference matrices, complex Hadamard matrices and complex equiangular tight frames

Chevallier, Fruchard & Vilcu: Envelopes of α-sections

Bokowski & al.: Selected open and solved problems in computational synthetic geometry

Bau: Reductions of 3-connected quadrangulations of the sphere

Barany & Por: Paths on the sphere without small angles

PART II Open Problem Notes. Zamfirescu T.: Two problems on cages for discs

Zamfirescu Carol T.: Seven problems on hypohamiltonian and almost hypohamiltonian graphs

Vilcu & Zamfirescu: Six problems on the length of the cut locus

Simoes-Pereira: Existence Problems for Matroidal Families

Funar: Cubical Pachner moves

Eckhoff: Problems in Discrete Geometry

Chevallier & Fruchard: What is the minimal cardinal of a family which shatters all d-subsets of a finite set?

Baskoro: Some open problems of Ramsey minimal graphs. .

Notes:

Includes bibliographical references.

ISBN:

3-319-28186-0