6 papers · 1 filter
Exact Homomorphism Thresholds Beyond Cliques
Xinqi Huang, Mingyuan Rong, Chong Shangguan
The chromatic threshold, originating in a question of Erdős and Simonovits, asks when a linear minimum-degree condition forces bounded chromatic number in H-free graphs. Motivated…
Sharp asymptotic bounds for uniform union-free hypergraphs
Miao Liu, Chong Shangguan, Chenyang Zhang
An -uniform hypergraph is called -union-free if any two distinct subsets of at most edges have distinct union. The study of union-free hypergraphs has multiple origins an…
Incidence theorems for multivariate polynomials over finite fields
Chong Shangguan, Yulin Yang, Tao Zhang
We study incidence problems for multivariate polynomials over a finite field . Given two families of -variate polynomials, we count the number of triples …
Stability with minuscule structure for chromatic thresholds
Jaehoon Kim, Hong Liu, Chong Shangguan +3
The chromatic threshold of a graph is the infimum of such that the chromatic number of every -vertex -free graph with minimum degree at least is boun…
Focal-free uniform hypergraphs and codes
Xinqi Huang, Chong Shangguan, Xiande Zhang +1
Motivated by the study of a variant of sunflowers, Alon and Holzman recently introduced focal-free hypergraphs. In this paper, we show that there is an interesting connection betwe…
Beyond chromatic threshold via the -theorem, and a sharp blow-up phenomenon
Hong Liu, Chong Shangguan, Jozef Skokan +1
We establish a novel connection between the well-known chromatic threshold problem in extremal combinatorics and the celebrated -theorem in discrete geometry. In particular,…