Shira Zerbib

activity

20122026

most citedEnvy-free cake division without assuming the players prefer nonempty pieces

21 citations · 37 across the 25 of their papers we have counts for

collaborators

38 papers

math.CO2026

The chromatic number of 3-stable Kneser graphs

Wei-Chia Chen, Alex Parker, Shira Zerbib

For an integer $s \geq 2$ , a subset $S \subseteq [n]$ is {\em $s$ -stable} if $min {j - i, n + i - j} \geq s$ for every $i, j \in S$ with $i < j$ . Denote the set of all $s$ -stable subs…

math.CO2026

Generalized Ramsey Numbers in the Hypercube

Emily Heath, Coy Schwieder, Shira Zerbib

We study the generalized Ramsey numbers $f (Q_{n}, C_{k}, q)$ , that is, the minimum number of colors needed to edge-color the hypercube $Q_{n}$ so that every copy of the cycle $C_{k}$ h…

math.CO2025

Ramsey Numbers in Kneser Graphs

Emily Heath, Grace McCourt, Alex Parker +2

We define the $r -Kneser Ramsey number$ $R_{r}^{KG} (s, t)$ as the minimum integer $n$ such that every red/blue edge-coloring of the Kneser graph $KG (n, r)$ …

math.CO2025

Odd Ramsey numbers of multipartite graphs and hypergraphs

Nicholas Crawford, Emily Heath, Owen Henderschedt +2

Given a hypergraph $G$ and a subhypergraph $H$ of $G$ , the \emph{odd Ramsey number} $r_{o dd} (G, H)$ is the minimum number of colors needed to edge-color $G$ so that every copy of $H…

math.CO2025

A topological product Tverberg Theorem

Andreas F. Holmsen, Grace McCourt, Daniel McGinnis +1

We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let $Δ$ denote the 8-dimensional simplex viewed as an a…

math.CO2024

Using the KKM theorem

Daniel McGinnis, Shira Zerbib

The KKM theorem, due to Knaster, Kuratowski, and Mazurkiewicz in 1929, is a fundamental result in fixed-point theory, which has seen numerous extensions and applications. In this p…

math.CO2024

Generalized Ramsey numbers of cycles, paths, and hypergraphs

Deepak Bal, Patrick Bennett, Emily Heath +1

Given a $k$ -uniform hypergraph $G$ and a set of $k$ -uniform hypergraphs $H$ , the generalized Ramsey number $f (G, H, q)$ is the minimum number of colors needed to…

math.CO2024

Improved Tverberg theorems for certain families of polytopes

Pablo Soberón, Shira Zerbib

A theorem of Grünbaum, which states that every $m$ -polytope is a refinement of an $m$ -simplex, implies the following generalization of Tverberg's theorem: if $f$ is a linear functi…

math.CO2023

Graphs with no even holes and no sector wheels are the union of two chordal graphs

Tara Abrishami, Eli Berger, Maria Chudnovsky +1

Sivaraman conjectured that if $G$ is a graph with no induced even cycle then there exist sets $X_{1}, X_{2} \subseteq V (G)$ satisfying $V (G) = X_{1} \cup X_{2}$ such that the induced graph…

math.CO2023

Looms

Ron Aharoni, Eli Berger, Joseph Briggs +2

A pair $(A, B)$ of hypergraphs is called orthogonal if $∣ a \cap b ∣ = 1$ for every pair of edges $a \in A$ and $b \in B$ . An orthogonal pair of hypergraphs is called a loom if each of…

math.CO2023★ 2 cited

Edge-coloring a graph $G$ so that every copy of a graph $H$ has an odd color class

Patrick Bennett, Emily Heath, Shira Zerbib

Recently, Alon introduced the notion of an $H$ -code for a graph $H$ : a collection of graphs on vertex set $[n]$ is an $H$ -code if it contains no two members whose symmetric differe…

math.CO2023★ 1 cited

New bounds on the generalized Ramsey number $f (n, 5, 8)$

Enrique Gomez-Leos, Emily Heath, Alex Parker +2

Let $f (n, p, q)$ denote the minimum number of colors needed to color the edges of $K_{n}$ so that every copy of $K_{p}$ receives at least $q$ distinct colors. In this note, we show $\fra…

math.CO2023

Bounds on piercing and line-piercing numbers in families of convex sets in the plane

Shira Zerbib

A family of sets has the $(p, q)$ property if among any $p$ members of it some $q$ intersect. It is shown that if a finite family of compact convex sets in $R^{2}$ has the $(p + 1, 2)$ …

math.CO2022

Matchings in matroids over abelian groups

Mohsen Aliabadi, Shira Zerbib

We formulate and prove matroid analogues of results concerning matchings in groups. A matching in an abelian group $(G, +)$ is a bijection $f : A \to B$ between two finite subsets $A,B…

math.CO2021

A Sparse colorful polytopal KKM Theorem

Daniel McGinnis, Shira Zerbib

Recently Soberón proved a far-reaching generalization of the colorful KKM Theorem due to Gale: let $n \geq k$ , and assume that a family of closed sets $(A^i_j\mid i\in [n], j\in [k]…

math.CO2021★ 2 cited

Non-uniform degrees and rainbow versions of the Caccetta-Häggkvist conjecture

Ron Aharoni, Eli Berger, Maria Chudnovsky +2

The Caccetta-Häggkvist conjecture (denoted below CHC) states that the directed girth (the smallest length of a directed cycle) $d g i r t h (D)$ of a directed graph $D$ on $n$ vertices i…

math.CO2021★ 3 cited

Improved bounds on a generalization of Tuza's conjecture

Abdul Basit, Daniel McGinnis, Henry Simmons +2

For an $r$ -uniform hypergraph $H$ , let $ν^{(m)} (H)$ denote the maximum size of a set~ $M$ of edges in $H$ such that every two edges in $M$ intersect in less than $m$ vertices, and l…

math.CO2021

Line transversals in families of connected sets the plane

Daniel McGinnis, Shira Zerbib

We prove that if a family of compact connected sets in the plane has the property that every three members of it are intersected by a line, then there are three lines intersecting…

math.CO2020

Rainbow paths and large rainbow matchings

Ron Aharoni, Eli Berger, Maria Chudnovsky +1

A conjecture of the first two authors is that $n$ matchings of size $n$ in any graph have a rainbow matching of size $n - 1$ . We prove a lower bound of $\frac{2}{3} n - 1$ , improving on…

math.CO2020★ 2 cited

Fractionally balanced hypergraphs and rainbow KKM theorems

Ron Aharoni, Eli Berger, Joseph Briggs +2

A d-partite hypergraph is called *fractionally balanced* if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex sid…

math.CO2020★ 1 cited

On Weak Flexibility in Planar Graphs

Bernard Lidický, Tomáš Masařík, Kyle Murphy +1

Recently, Dvořák, Norin, and Postle introduced flexibility as an extension of list coloring on graphs [JGT 19']. In this new setting, each vertex $v$ in some subset of $V (G)$ has a…

math.CO2020

Tournaments and the Strong Erdős-Hajnal Property

Eli Berger, Krzysztof Choromanski, Maria Chudnovsky +1

A conjecture of Alon, Pach and Solymosi, which is equivalent to the celebrated Erdős-Hajnal Conjecture, states that for every tournament $S$ there exists $ε (S) > 0$ such that if $T$ …

math.CO2018

Large triangle packings and Tuza's conjecture in sparse random graphs

Patrick Bennett, Andrzej Dudek, Shira Zerbib

The triangle packing number $ν (G)$ of a graph $G$ is the maximum size of a set of edge-disjoint triangles in $G$ . Tuza conjectured that in any graph $G$ there exists a set of at mo…

math.CO2018

On Lusztig-Dupont homology of flag complexes

Roy Meshulam, Shira Zerbib

Let $V$ be an $n$ -dimensional vector space over the finite field of order $q$ . The spherical building $X_{V}$ associated with $G L (V)$ is the order complex of the nontrivial linear su…

The chromatic number of 3-stable Kneser graphs

Generalized Ramsey Numbers in the Hypercube

Ramsey Numbers in Kneser Graphs

Odd Ramsey numbers of multipartite graphs and hypergraphs

A topological product Tverberg Theorem

Using the KKM theorem

Generalized Ramsey numbers of cycles, paths, and hypergraphs

Improved Tverberg theorems for certain families of polytopes

Graphs with no even holes and no sector wheels are the union of two chordal graphs

Looms

Edge-coloring a graph G so that every copy of a graph H has an odd color class

New bounds on the generalized Ramsey number f(n,5,8)

Bounds on piercing and line-piercing numbers in families of convex sets in the plane

Matchings in matroids over abelian groups

A Sparse colorful polytopal KKM Theorem

Non-uniform degrees and rainbow versions of the Caccetta-Häggkvist conjecture

Improved bounds on a generalization of Tuza's conjecture

Line transversals in families of connected sets the plane

Rainbow paths and large rainbow matchings

Fractionally balanced hypergraphs and rainbow KKM theorems

On Weak Flexibility in Planar Graphs

Tournaments and the Strong Erdős-Hajnal Property

Large triangle packings and Tuza's conjecture in sparse random graphs

On Lusztig-Dupont homology of flag complexes

Edge-coloring a graph $G$ so that every copy of a graph $H$ has an odd color class

New bounds on the generalized Ramsey number $f (n, 5, 8)$