Hong Liu

activity

20102026

most citedUpper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube

58 citations · 220 across the 56 of their papers we have counts for

collaborators

Showing 2022Show all

8 papers · 1 filter

math.CO2022

Stability through non-shadows

Jun Gao, Hong Liu, Zixiang Xu

We study families $F \subseteq 2^{[n]}$ with restricted intersections and prove a conjecture of Snevily in a stronger form for large $n$ . We also obtain stability results…

math.CO2022★ 2 cited

Rainbow cycles in properly edge-colored graphs

Jaehoon Kim, Joonkyung Lee, Hong Liu +1

We prove that every properly edge-colored $n$ -vertex graph with average degree at least $100 (lo g n)^{2}$ contains a rainbow cycle, improving upon $(lo g n)^{2 + o (1)}$ bound due to To…

math.CO2022

Crux, space constraints and subdivisions

Seonghyuk Im, Jaehoon Kim, Younjin Kim +1

For a given graph $H$ , its subdivisions carry the same topological structure. The existence of $H$ -subdivisions within a graph $G$ has deep connections with topological, structural…

math.CO2022

Disjoint isomorphic balanced clique subdivisions

Irene Gil Fernández, Joseph Hyde, Hong Liu +2

A thoroughly studied problem in Extremal Graph Theory is to find the best possible density condition in a host graph $G$ for guaranteeing the presence of a particular subgraph $H$ …

math.CO2022★ 11 cited

On a rainbow extremal problem for color-critical graphs

Debsoumya Chakraborti, Jaehoon Kim, Hyunwoo Lee +2

There has been extensive studies on the following question: given $k$ graphs $G_{1}, \dots, G_{k}$ over a common vertex set of size $n$ , what conditions on $G_{i}$ ensures a `colorful' co…

math.CO2022

A proof of Frankl's conjecture on cross-union families

Stijn Cambie, Jaehoon Kim, Hong Liu +1

The families $F_{0}, \dots, F_{s}$ of $k$ -element subsets of $[n] := {1, 2, \dots, n}$ are called cross-union if there is no choice of $F_0\in \mathcal F_0, \ldots, F_s\…

math.CO2022

Exponential decay of intersection volume with applications on list-decodability and Gilbert-Varshamov type bound

Jaehoon Kim, Hong Liu, Tuan Tran

We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) we…

math.CO2022

How to build a pillar: a proof of Thomassen's conjecture

Irene Gil Fernández, Hong Liu

Carsten Thomassen in 1989 conjectured that if a graph has minimum degree more than the number of atoms in the universe ( $δ (G) \geq 1 0^{1 0^{10}}$ ), then it contains a pillar, which is…