6 papers
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 c…
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…
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 le…
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…
On the quadratic 8-edge case of the Brown-ErdÅs-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, ErdÅs and Sós conjectured in 1…
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:=…