In this paper, we study the fractional behavior of finite families of axis-parallel boxes, or boxes for short.
Oct 2, 2014 · Abstract:Let \mathcal{F} be a family of n axis-parallel boxes in \mathbb{R}^d and \alpha\in (1-1/d,1] a real number.
Introduction and results. According to the classical theorem of Helly [1], if every d + 1-element subfamily of a finite family of convex sets in Rd has ...
Our aim is to prove a statement similar to the. Fractional Helly Theorem. The intersection graph GF of a finite family F of boxes is a graph whose vertex set is ...
Let $\mathcal{F}$ be a family of $n$ axis-parallel boxes in $\mathbb{R}^d$ and $\alpha\in (1-1/d,1]$ a real number. There exists a real number $\beta(\alpha ) ...
Oct 22, 2024 · Their aim was to prove the following statement similar to the Fractional Helly Theorem [4]: "Let F be a family of n axis-parallel boxes in R d ...
Nov 26, 2019 · Question 1 is quite easy. Just project the family of boxes onto each of the d dimensions & apply Helly's theorem for each of these 1 ...
A fractional Helly theorem for boxes · I. Bárány, F. Fodor, +3 authors. A. Pór · Published in Computational geometry 2 October 2014 · Mathematics.
In our recent paper [1] we prove a fractional Helly type theorem for boxes in Rd. This short note is to acknowledge priority: in 1980 Meir Katchalski [4] proved ...
Aug 23, 2021 · A classical result of Eckhoff in 1988 provided an optimal fractional Helly theorem for axis-aligned boxes, which are Cartesian products of line ...