5 papers
Tight Staircase Bounds for Cyclic Subsets below Dirac's Threshold
Hong Liu, Mengyuan Niu, Lanchao Wang +1
Let denote the number of cyclic subsets in a graph , which are subsets that induce a Hamiltonian subgraph. Draganić, Keevash and Müyesser recently proved…
The sharp threshold for rainbow stackings of random edge-colourings
Hong Liu, Guorui Ma, Yangrui Xiang +1
A rainbow stacking of independent, uniformly random -edge-colourings of is a tuple of vertex permutations that superimposes the colourings such that no two edges of th…
Structural Reductions for Monochromatic Matchings and Ramsey Tilings
Hong Liu, Maksim Turevskii, Lanchao Wang +1
The Alon--Frankl--Lovász theorem determines the chromatic number of Kneser hypergraphs; equivalently, it gives the sharp minimum size of a monochromatic matching in every edge-colo…
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…
Infinitely many groups exhibiting intermediate growth in maximal sum-free sets
József Balogh, Ramon I. Garcia, Hong Liu +1
Given an Abelian groups , denote the size of its largest sum-free subset and the number of maximal sum-free sets in . Confirming a prediction by Liu and…