7 citations · 10 across the 20 of their papers we have counts for
12 papers · 1 filter
Colored Turán densities and finite directed templates
Nannan Chen, Ander Lamaison, Heng Li +1
Classical Turán theory relates the asymptotic extremal problem for an ordinary forbidden graph to its chromatic number. This principle fails when a forbidden copy must respect pres…
Turing universality, computability, and incompleteness in hypergraph Turán theory
Heng Li, Xizhi Liu
Given a finite family of forbidden -graphs, the Turán problem asks for the maximum asymptotic edge density of -free -graphs and the structure of near…
Nearly Sharp Bounds for Lattice Coverings by Convex Bodies
Heng Li, Xizhi Liu
For an -dimensional convex body , let denote its lattice covering density, and let and be the corresponding worst-ca…
Forcing Quasirandomness via Rooted F-Densities
Heng Li, Xizhi Liu
Let be a finite graph with at least one edge, and let be a graphon. We show that if the density of rooted at each edge is almost everywhere constant, then either $t(F,W…
Intervals of uniform Turán densities
Heng Li, Xizhi Liu, Oleg Pikhurko
We prove that the set of uniform Turán densities of possibly infinite families of -graphs contains a terminal interval: there exists such that $[1-…
A Higher-Order Clique Density Theorem
Heng Li, Hong Liu, Yixiao Zhang
Reiher's clique density theorem determines the sharp lower envelope for the density of at fixed edge density. We prove a higher-order version in which the prescribed quantity…
Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity
Heng Li, Hong Liu, Xizhi Liu +1
The supersaturation problem asks, for a fixed -graph , for the minimum number of copies of in an -vertex -graph with $\ex(n,\mathcal F)+q$ edges.…
On Mubayi's Polynomial-Ideal Conjecture and a Hypergraph Turán Theorem
Heng Li, Xizhi Liu
Among the many proofs of Turán's classical theorem, one particularly surprising proof due to Li and Li uses ideals in polynomial rings to record missing edges. Motivated by their p…
Sharp bounds for minimal dependencies of linear-form powers
Heng Li, Xizhi Liu
Motivated by the dimension-bound part of a problem of Bukh, we study Veronese circuits: how large can the span of linear forms be if their -th powers are minimally linearly…
On a hypergraph Turán problem of Balogh-Bohman-Bollobás-Zhao
Heng Li, Jie Ma, Tianhen Wang +2
Let and be disjoint sets with and for , and let be the -graph on whose edges are the -subsets containing or…
From Halin's Edge Removability to Matching Removability in -Connected Graphs
Hengzhe Li, Mingming Zhou, Shinya Fujita +1
We study matching-removability under the degree/connectivity regime of Halin's theorem, which asserts that every -connected graph with minimum degree contains…
A single -graph with infinite stability number
Heng Li, Xizhi Liu
The stability number of a forbidden family measures how many different structures are needed to approximate all near-extremal constructions avoiding it. An infinite stability numbe…