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10/26/2022
Turán graphs with bounded matching number
We determine the maximum possible number of edges of a graph with n vert...
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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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11/18/2021
A Variant of the VC-dimension with Applications to Depth-3 Circuits
We introduce the following variant of the VC-dimension. Given S ⊆{0, 1}^...
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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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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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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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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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11/02/2018
Diversity
Given a family F⊂ 2^[n], its diversity is the number of sets not contai...
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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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04/10/2018