10 citations · 38 across the 54 of their papers we have counts for
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Disjoint pairs in set systems and combinatorics of low rank matrices
Zach Hunter, Aleksa Milojević, Benny Sudakov +1
We study and solve several problems in two closely related settings: set families in with many disjoint pairs of sets and low rank matrices with many zero entries. - More…
Long induced paths in -free graphs
Zach Hunter, Aleksa Milojević, Benny Sudakov +1
More than 40 years ago, Galvin, Rival and Sands showed that every -free graph containing an -vertex path must contain an induced path of length , where $f(n)\to…
Explicit constructions of optimal blocking sets and minimal codes
Anurag Bishnoi, István Tomon
A strong -blocking set in a projective space is a set of points that intersects each codimension- subspace in a spanning set of the subspace. We present an explicit construct…
Large Cuts in Hypergraphs via Energy
Eero Räty, István Tomon
A simple probabilistic argument shows that every -uniform hypergraph with edges contains an -partite subhypergraph with at least edges. The celebrated r…
Bisection Width, Discrepancy, and Eigenvalues of Hypergraphs
Eero Räty, István Tomon
A celebrated result of Alon from 1993 states that any -regular graph on vertices (where ) has a bisection with at most $\frac{dn}{2}(\frac{1}{2}-Ω(\frac{1}{\sq…
The number of symmetric chain decompositions
István Tomon
We prove that the number of symmetric chain decompositions of the Boolean lattice is Furthermore, the number of symmetric chain…
Point-variety incidences, unit distances and Zarankiewicz's problem for algebraic graphs
Aleksa Milojević, Benny Sudakov, István Tomon
In this paper we study the number of incidences between points and varieties in , where is an arbitrary field, assuming the incidence graph conta…
The Quantitative Fractional Helly theorem
Nóra Frankl, Attila Jung, István Tomon
Two celebrated extensions of Helly's theorem are the Fractional Helly theorem of Katchalski and Liu (1979) and the Quantitative Volume theorem of Bárány, Katchalski, and Pach (1982…
Kővári-Sós-Turán theorem for hereditary families
Zach Hunter, Aleksa Milojević, Benny Sudakov +1
The celebrated Kővári-Sós-Turán theorem states that any -vertex graph containing no copy of the complete bipartite graph has at most edges. In the pas…
Incidence bounds via extremal graph theory
Aleksa Milojević, István Tomon, Benny Sudakov
The study of counting point-hyperplane incidences in the -dimensional space was initiated in the 1990's by Chazelle and became one of the central problems in discrete geometry.…