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

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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 |