3 citations · 11 across the 17 of their papers we have counts for
7 papers · 2 filters
The and properties in families of fat sets in the plane
Shiliang Gao, Shira Zerbib
A family of sets satisfies the property if among every members of it some intersect. Given a number , a set is called -fat if t…
Fair division with multiple pieces
Kathryn Nyman, Francis Edward Su, Shira Zerbib
Given a set of players we consider problems concerning envy-free allocation of collections of pieces from a given set of goods or chores. We show that if and each…
Piercing Numbers in Approval Voting
Francis Edward Su, Shira Zerbib
We survey a host of results from discrete geometry that have bearing on the analysis of geometric models of approval voting. Such models view the political spectrum as a geometric…
Colorful coverings of polytopes and piercing numbers of colorful d-intervals
Florian Frick, Shira Zerbib
We prove a common strengthening of Bárány's colorful Carathéodory theorem and the KKMS theorem. In fact, our main result is a colorful polytopal KKMS theorem, which extends a color…
An improved bound in Vizing's conjecture
Shira Zerbib
A well-known conjecture of Vizing is that for any pair of graphs , where is the domination number and is the Cartesian product…
Piercing axis-parallel boxes
Maria Chudnovsky, Sophie Spirkl, Shira Zerbib
Let $\F$ be a finite family of axis-parallel boxes in such that $\F$ contains no pairwise disjoint boxes. We prove that if $\F$ contains a subfamily $\M$ of pairwi…