From the 1 of 6 linked papers with an AI index.
6 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.
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…
Optimal stability results on color-biased Hamilton cycles
Wenchong Chen, Mingyuan Rong, Zixiang Xu
We investigate Hamilton cycles in edge-colored graphs with \( r \) colors, focusing on the notion of color-bias (discrepancy), the maximum deviation from uniform color frequencies…
Largest dyadic dual VC-dimension of non-piercing families
Xinqi Huang, Yuzhen Qi, Mingyuan Rong +1
The dyadic dual VC-dimension of a set system \( \mathcal{F} \) is the largest integer \( \ell \) such that there exist \( \ell \) sets \( F_1, F_{2}, \dots, F_\ell \in \mathcal{F}…
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…
Sublinear hitting sets for some geometric graphs
Xinbu Cheng, Xinqi Huang, Mingyuan Rong +1
For an -vertex graph , let denote the smallest size of a subset of such that it intersects every maximum independent set of . A conjecture posed by Bollobás…