5 papers
On the spectrum and structure of blowup thresholds
Xinqi Huang, Hong Liu, Mingyuan Rong
The chromatic threshold of ErdÅs and Simonovits asks when a minimum-degree condition forces every \(H\)-free graph to have bounded chromatic number. Thomassen's homomorphism thres…
Triangle packings in randomly perturbed graphs
Xinbu Cheng, Hong Liu, Lanchao Wang +1
The longstanding Nash-Williams conjecture asserts that every -divisible graph with admits a triangle decomposition. In the random setting, Frankl and Rödl…
Interpolating chromatic and homomorphism thresholds
Xinqi Huang, Hong Liu, Mingyuan Rong +1
The problem of chromatic thresholds seeks for minimum degree conditions that ensure -free graphs to have a bounded chromatic number, or equivalently a bounded size homomorphic i…
Clique density vs blowups
Domagoj BradaÄ, Hong Liu, Zhuo Wu +1
A well-known theorem of Nikiforov asserts that any graph with a positive -density contains a logarithmic blowup of . In this paper, we explore variants of Nikiforov's r…
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,…