Author

Miao Liu

2 papers indexed here

We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.

Not the right person? Other researchers publish under this name.

Preprint Sep 2026

A proof of Chv\'atal's conjecture via a sharp correlation inequality

We prove Chv\'atal's conjecture, posed in 1972: every hereditary family of subsets of a finite set has a largest intersecting subfamily that is a star. More generally, we prove a sharp correlation inequality for increasing Boolean functions $f,g:\{0,1\}^n\to\{0,1\}$. Writing $g^*(x)=1-g(1-x)$, we show that $$ \sum_{\va...

Fan Chang, Hong Liu, Miao Liu · 4 citations · ⚡3

Preprint Sep 2026

Extremal problems for cancellative and locally thin hypergraphs

We study Tur\'an-type extremal problems for cancellative and locally thin uniform hypergraphs. An $r$-uniform hypergraph is $t$-cancellative if $(\cup_{i=1}^t A_i)\cup B\ne (\cup_{i=1}^t A_i)\cup C$ whenever $A_1,\ldots,A_t,B,C$ are distinct edges. Let $C_t(n,r)$ denote the maximum number of edges in such a hypergraph...

Miao Liu, Chong Shangguan, Chen-Yang Zhang · 0 citations