5 citations · 5 across the 27 of their papers we have counts for
10 papers · 1 filter
Covering large-dimensional Euclidean spaces by random translates of a given convex body
Boris Bukh, Jun Gao, Xizhi Liu +2
Determining the minimum density of a covering of by Euclidean unit balls as is a major open problem, with the best known results being the lower bound…
Semi-inducibility of 4-vertex graphs
Levente Bodnár, Oleg Pikhurko
For a graph whose edges are coloured blue or red, the -semi-inducibility problem asks for the maximum, over all graphs of given order , of the number of injections fr…
New upper bound for lattice covering by spheres
Jun Gao, Xizhi Liu, Oleg Pikhurko +1
We show that there exists a lattice covering of by Eucledian spheres of equal radius with density as , where \begin{align*} β:= \…
Some exact inducibility-type results for graphs via flag algebras
Levente Bodnár, Oleg Pikhurko
The -edge-inducibility problem asks for the maximum number of -subsets inducing exactly edges that a graph of given order can have. Using flag algebras and…
The Turán density of short tight cycles
Levente Bodnár, Jared León, Xizhi Liu +1
The -uniform tight -cycle is the -graph on consisting of all consecutive triples in the cyclic order. Let be either…
Convergence of spectra of digraph limits
Jan Grebík, Daniel Král', Xizhi Liu +2
The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness…
On the quadratic 8-edge case of the Brown-Erdős-Sós problem
Oleg Pikhurko, Shumin Sun
Let be the maximum number of edges in an -vertex -uniform hypergraph containing no edges on at most vertices. Brown, Erdős and Sós conjectured in 197…
Some exact values of the inducibility and statistics constants for hypercubes
Levente Bodnár, Oleg Pikhurko
We consider two types of problems: maximising, over subsets , the density of -subcubes in the -hypercube graph that span a subgraph such that $S\cap…
A note on the minimum size of Turán systems
Xizhi Liu, Oleg Pikhurko
For positive integers , a \emph{Turán -system} is an -vertex -graph in which every set of vertices contains at least one edge. Let denote…
Fractional Divisibility of Spheres with Partially Generic Sets of Rotations
Jan Grebík, Christian Ikenmeyer, Oleg Pikhurko
We say that an r-tuple of special orthogonal matrices fractionally divides the -dimensional sphere if there is a non-constant function in $L^…