DCG
2007
13 years 5 months ago
2007
Given a sphere of any radius r in an n-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the...
DCG
2007
13 years 5 months ago
2007
Steinitz’s Theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of ...
DCG
2007
13 years 5 months ago
2007
DCG
2007
13 years 5 months ago
2007
In this paper we study the following simple and mind-puzzling problem: Can a model train car, which runs along an intricate track complete a full cycle around it? In our paper a t...
DCG
2007
13 years 5 months ago
2007
We consider polytopes in Rn that are generated by N vectors in Rn whose coordinates are independent subgaussian random variables. (A particular case of such polytopes are symmetri...
DCG
2007
13 years 5 months ago
2007
DCG
2007
13 years 5 months ago
2007
In this paper we investigate the Erd¨os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We pr...
DCG
2007
13 years 5 months ago
2007
The coincidence site lattice (CSL) problem and its generalization to Z-modules in Euclidean 3-space is revisited, and various results and conjectures are proved in a unified way, ...
DCG
2007
13 years 5 months ago
2007
We establish a new lower bound for the number of sides required for the component curves of simple Venn diagrams made from polygons. Specifically, for any n-Venn diagram of conve...
DCG
2007
13 years 5 months ago
2007
