7 citations · 37 across the 71 of their papers we have counts for
16 papers · 1 filter
Andr{á}sfai--Erdős--Sós theorem under max-degree constraints
Xizhi Liu, Sijie Ren, Jian Wang
We establish the following strengthening of the celebrated Andr{á}sfai--Erdős--Sós theorem: If is an -vertex -free graph whose minimum degree and maximum deg…
Tetrahedron Conjecture in the -norm
Levente Bodnár, Wanfang Chen, Jinghua Deng +5
The famous Tetrahedron Conjecture of Turán from the 1940s asserts that the number of edges in an -vertex -graph without the tetrahedron, the complete -graph on four vertic…
Odd hypergraph Mantel theorems
Jianfeng Hou, Xizhi Liu, Yixiao Zhang +2
A classical result of Sidorenko (1989) shows that the Turán density of every -uniform hypergraph with three edges is bounded from above by . For even , this bound is tig…
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 a refinement of the Ahlswede--Katona Theorem
Jianfeng Hou, Xizhi Liu, Yixiao Zhang
A classical theorem of Ahlswede and Katona determines the maximum density of the -edge star in a graph with a given edge density. Motivated by its application in hypergraph Turá…
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:= \…