We prove that any finite set of half-planes can be colored by two colors so that every point of the plane, which belongs to at least three half-planes in the set, is covered by ha...
The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) (0, 1] such that no matter how we map the vertices of H into Rd , there is a point covered...
Jacob Fox, Mikhail Gromov, Vincent Lafforgue, Assa...
Abstract. We give an overview of the main ideas and tools that have been employed in uncertain geometry. We show how several recognition problems in computer vision can be translat...
We study approximation solutions for the densest k-subgraph problem (DS-k) on several classes of intersection graphs. We adopt the concept of -quasi elimination orders, introduced ...
In Graph Minors III, Robertson and Seymour write:"It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal -- indeed, w...