7 citations · 15 across the 16 of their papers we have counts for
21 papers
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…
On a hypergraph Mantel theorem
Xizhi Liu
An -graph is a triangle if there exists a positive integer such that it is isomorphic to the following -graph with three edges: \begin{align*} \left…
Tiling in dense graphs
Nannan Chen, Xizhi Liu, Lin Sun +1
We determine asymptotically the two extremal constructions for the tiling problem of the -shaped tree. In particular, the first extremal construction is close to the complement…
Density Hajnal--Szemerédi theorem for cliques of size four
Jianfeng Hou, Caiyun Hu, Xizhi Liu +1
The celebrated Corrádi--Hajnal Theorem~\cite{CH63} and the Hajnal--Szemerédi Theorem~\cite{HS70} determined the exact minimum degree thresholds for a graph on vertices to conta…
Generalized Andrásfai--Erdős--Sós theorems for odd cycles
Zian Chen, Jianfeng Hou, Caiyun Hu +1
In this note, we establish Andrásfai--Erdős--Sós-type stability theorems for two generalized Turán problems involving odd cycles, both of which are extensions of the Erdős Pentagon…
Uniquely colorable hypergraphs
Xizhi Liu, Jie Ma, Tianhen Wang +1
An -uniform hypergraph is uniquely -colorable if there exists exactly one partition of its vertex set into parts such that every edge contains at most one vertex from eac…