7 papers · 1 filter
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…
Canonical Ramsey numbers of sparse graphs
Lior Gishboliner, Aleksa Milojević, Benny Sudakov +1
The canonical Ramsey theorem of Erdős and Rado implies that for any graph , any edge-coloring (with an arbitrary number of colors) of a sufficiently large complete graph c…
Larger Nearly Orthogonal Sets over Finite Fields
Ishay Haviv, Sam Mattheus, Aleksa Milojević +1
For a field and integers and , a set is called -nearly orthogonal if its members are non-self-orthogonal and every ve…
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…
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.…