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08/31/2023
Erdős–Ko–Rado type results for partitions via spread approximations
In this paper, we address several Erdős–Ko–Rado type questions for famil...
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09/10/2022
Octopuses in the Boolean cube: families with pairwise small intersections, part I
Let ℱ_1, …, ℱ_ℓ be families of subsets of {1, …, n}. Suppose that for di...
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06/03/2022
Erdős Matching Conjecture for almost perfect matchings
In 1965 Erdős asked, what is the largest size of a family of k-elements ...
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02/18/2022
Sketching Distances in Monotone Graph Classes
We study the problems of adjacency sketching, small-distance sketching, ...
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01/11/2022
Perfect matchings in down-sets
In this paper, we show that, given two down-sets (simplicial complexes) ...
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12/19/2021
On the Erdős-Purdy problem and the Zarankiewitz problem for semialgebraic graphs
Erdős and Purdy, and later Agarwal and Sharir, conjectured that any set ...
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12/08/2021
On anti-stochastic properties of unlabeled graphs
We study vulnerability of a uniformly distributed random graph to an att...
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08/01/2021
Choice number of Kneser graphs
In this short note, we show that for any ϵ >0 and k<n^0.5-ϵ the choice n...
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08/01/2021
On the maximum number of distinct intersections in an intersecting family
For n > 2k ≥ 4 we consider intersecting families ℱ consisting of k-subse...
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06/09/2021
Best possible bounds on the number of distinct differences in intersecting families
For a family ℱ, let 𝒟(ℱ) stand for the family of all sets that can be ex...
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06/09/2021
Uniform intersecting families with large covering number
A family ℱ has covering number τ if the size of the smallest set interse...
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12/28/2020
Trivial colors in colorings of Kneser graphs
We show that any proper coloring of a Kneser graph KG_n,k with n-2k+2 co...
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09/30/2020
Intersection theorems for triangles
Given a family of sets on the plane, we say that the family is intersect...
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08/17/2020
Binary scalar products
Let A,B ⊆ℝ^d both span ℝ^d such that ⟨ a, b ⟩∈{0,1} holds for all a ∈ A,...
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04/18/2020
Intersection theorems for (-1,0,1)-vectors
In this paper, we investigate Erdős–Ko–Rado type theorems for families o...
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04/18/2020
Maximal degrees in subgraphs of Kneser graphs
In this paper, we study the maximum degree in non-empty induced subgraph...
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04/18/2020
Almost intersecting families
Let n > k > 1 be integers, [n] = {1, …, n}. Let ℱ be a family of k-subse...
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04/09/2020
The VC-dimension of k-vertex d-polytopes
In this short note, we show that the VC-dimension of the class of k-vert...
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01/07/2020
Rainbow matchings in k-partite hypergraphs
In this paper, we prove a conjecture of Aharoni and Howard on the existe...
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05/20/2019
Sharp results concerning disjoint cross-intersecting families
For an $n$-element set $X$ let $\binom{X}{k}$ be the collection of all i...
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01/26/2019
Beyond the Erdős Matching Conjecture
A family F⊂[n] k is U(s,q) of for any F_1,..., F_s∈ F we have |F_1∪...∪...
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01/12/2019
Simple juntas for shifted families
We say that a family F of k-element sets is a j-junta if there is a set...
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12/12/2018
The Crossing Tverberg Theorem
Tverberg's theorem is one of the cornerstones of discrete geometry. It s...
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11/02/2018
Diversity
Given a family F⊂ 2^[n], its diversity is the number of sets not contai...
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10/02/2018
Sharp bounds for the chromatic number of random Kneser graphs
Given positive integers n> 2k, a Kneser graph KG_n,k is a graph whose ve...
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10/01/2018
Degree versions of theorems on intersecting families via stability
The matching number of a family of subsets of an n-element set is the ma...
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08/03/2018
Incompatible intersection properties
Let F⊂ 2^[n] be a family in which any three sets have non-empty interse...
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07/20/2018
Optimal Bounds on the VC-dimension
The VC-dimension of a set system is a way to capture its complexity and ...
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04/10/2018
New inequalities for families without k pairwise disjoint members
Some best possible inequalities are established for k-partition-free fam...
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12/08/2017
Tilings of the plane with unit area triangles of bounded diameter
There exist tilings of the plane with pairwise noncongruent triangles of...
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11/28/2017
When are epsilon-nets small?
In many interesting situations the size of epsilon-nets depends only on ...
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11/13/2017
Tilings with noncongruent triangles
We solve a problem of R. Nandakumar by proving that there is no tiling o...
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10/06/2017
Structure and properties of large intersecting families
We say that a family of k-subsets of an n-element set is intersecting, i...
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09/29/2017
Regular Intersecting Families
We call a family of sets intersecting, if any two sets in the family int...
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09/08/2017