3 papers
math.CO2026
Colour diversity in spanning structures under Dirac-type conditions
Xinbu Cheng, Xinqi Huang, Hong Liu +2
Finding spanning structures with many distinct colours in properly edge-coloured graphs is a central theme in extremal combinatorics. A classical result of Andersen shows that ever…
math.CO2025
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}…
math.CO2025
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…