From the 1 of 5 linked papers with an AI index.
5 papers
Exact Homomorphism Thresholds Beyond Cliques
Xinqi Huang, Mingyuan Rong, Chong Shangguan
The paper determines the exact homomorphism thresholds for a broad family of non‑complete forbidden graphs, extending previous results that were limited to cliques.
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 …
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…
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 bo…
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…