Combinatorial Properties and Recognition of Unit Square Visibility Graphs [0.03%]
单元正方形可视图的组合性质和识别算法
Katrin Casel,Henning Fernau,Alexander Grigoriev et al.
Katrin Casel et al.
Unit square visibility graphs (USV) are described by axis-parallel visibility between unit squares placed in the plane. If the squares are required to be placed on integer grid coordinates, then USV become unit square grid visibility graphs...
Alan Arroyo,Fabian Klute,Irene Parada et al.
Alan Arroyo et al.
A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G + e ...
Cusp Density and Commensurability of Non-arithmetic Hyperbolic Coxeter Orbifolds [0.03%]
非余扭双曲考赫尔 orbifold 的尖点密度和可公度性
Edoardo Dotti,Simon T Drewitz,Ruth Kellerhals
Edoardo Dotti
For three distinct infinite families ( R m ) , ( S m ) , and ( T m ) of non-arithmetic 1-cusped hyperbolic Coxeter 3-orbifolds, we prove incommensurability for a pair of elements X k and Y l belonging to the same sequence and for most ...
Lonely Points in Simplices [0.03%]
单形中的孤立点
Maximilian Jaroschek,Manuel Kauers,Laura Kovács
Maximilian Jaroschek
Given a lattice L ⊆ Z m and a subset A ⊆ R m , we say that a point in A is lonely if it is not equivalent modulo L to another point of A. We are interested in identifying lonely points for specific choices of L when A is a d...
Jean-Daniel Boissonnat,Ramsay Dyer,Arijit Ghosh et al.
Jean-Daniel Boissonnat et al.
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A , and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H...
Georg Loho,Raman Sanyal
Georg Loho
Bárány's colorful generalization of Carathéodory's Theorem combines geometrical and combinatorial constraints. Kalai-Meshulam (2005) and Holmsen (2016) generalized Bárány's theorem by replacing color classes with matroid constraints. I...
Uli Wagner,Emo Welzl
Uli Wagner
Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P ' of P containing all extrem...
Aruni Choudhary,Wolfgang Mulzer
Aruni Choudhary
Tverberg's theorem states that for any k ≥ 2 and any set P ⊂ R d of at least ( d + 1 ) ( k - 1 ) + 1 points in d dimensions, we can partition P into k subsets whose convex hulls have a non-empty intersection. The associated ...
Distance Bounds for High Dimensional Consistent Digital Rays and 2-D Partially-Consistent Digital Rays [0.03%]
高维一致数字射线和二维部分一致性数字射线的距离界限
Man-Kwun Chiu,Matias Korman,Martin Suderland et al.
Man-Kwun Chiu et al.
We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in Z d . The construction must be consistent (that is, satisfy the natural extension of the Euclidean ax...
Guest Editors' Foreword [0.03%]
客座主编致辞
Sergio Cabello,Danny Z Chen
Sergio Cabello