5 citations · 5 across the 27 of their papers we have counts for
10 papers · 1 filter
The quadratic Brown--Erdős--Sós problem for 3-uniform hypergraphs with 8 and 9 edges
Levente Bodnár, Oleg Pikhurko, Shumin Sun +2
The famous and actively studied problem of Brown--Erdős--Sós from 1973 asks for , the maximum number of edges in an -graph with vertices in which no vert…
An improved bound on the minimum size of Turán -systems
Jun Gao, Peiru Kuang, Oleg Pikhurko +1
For positive integers , let denote the minimum number of edges in an -uniform hypergraph on vertices such that every -set of vertices contains at lea…
Intervals of uniform Turán densities
Heng Li, Xizhi Liu, Oleg Pikhurko
We prove that the set of uniform Turán densities of possibly infinite families of -graphs contains a terminal interval: there exists such that $[1-…
The inducibility of 6-vertex graphs
Levente Bodnár, Jun Gao, Jared León +3
The inducibility constant of a graph is the asymptotically maximum induced density of in a growing sequence of graphs. This paper systematically investigates the ca…
Strong non-principality of positive codegree Turán density
Levente Bodnár, Jun Gao, Oleg Pikhurko +2
The \emph{minimum positive codegree} of a -graph is the minimum, over all -sets that lie in at least one edge, of the number of edges containing that s…
A note on the Ratio and Inertia Bounds for the -Independence Number
Jun Gao, Jie Ma, Oleg Pikhurko
The -th power of a graph is the graph on the same vertex set where the edge set consists of those pairs of distinct vertices of that are at distance at most fr…
Intervals of hypergraph Turán densities
Xizhi Liu, Oleg Pikhurko
We prove that, for every integer , the set of Turán densities of (possibly infinite) families of -graphs contains non-degenerate intervals, including an…
A zero-one law for the spectral gap property of pairs in SU(2)
Oleg Pikhurko, Kohki Sakamoto
For , Gamburd, Jakobson, and Sarnak [J. Eur. Math. Soc. 1, 51-85 (1999)] conjectured that almost every -tuple in has a spectral gap. Toward this conjec…
On problems of Erdős and Baumann-Briggs on minimising the density of -cliques in graphs with forbidden subgraphs
Levente Bodnár, Oleg Pikhurko
Using flag algebras, we prove that the minimum density of -cliques in a large graph without an independent set of size is , thus resolving a new case…
Rational codegree Turán density of hypergraphs
Jun Gao, Oleg Pikhurko, Mingyuan Rong +1
Let be a -graph (i.e. a -uniform hypergraph). Its minimum codegree is the largest integer such that every -subset of is contained in at lea…