Jaehoon Kim

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6 papers · 1 filter

math.CO2025

Stability with minuscule structure for chromatic thresholds

Jaehoon Kim, Hong Liu, Chong Shangguan +3

The chromatic threshold $δ_{χ} (H)$ of a graph $H$ is the infimum of $d > 0$ such that the chromatic number of every $n$ -vertex $H$ -free graph with minimum degree at least $d n$ is boun…

math.CO2025

On the order of intersecting hypergraphs

Stijn Cambie, Jaehoon Kim, Hyunwoo Lee +2

Determining the maximum number of edges in an intersecting hypergraph on a fixed ground set under additional constraints is one of the central topics in extremal combinatorics. In…

math.CO2024

New lower bound on ball packing density in high-dimensional hyperbolic spaces

Irene Gil Fernández, Jaehoon Kim, Hong Liu +1

We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor Ω(m…

math.CO2024

Ore-type conditions for existence of a jellyfish in a graph

Jaehoon Kim, Alexandr Kostochka, Ruth Luo

The famous Dirac's Theorem states that for each $n \geq 3$ every $n$ -vertex graph $G$ with minimum degree $δ (G) \geq n /2$ has a hamiltonian cycle. When $δ (G) < n /2$ , this cannot be gu…

math.CO2024

Optimal bounds on the polynomial Schur's theorem

Jaehoon Kim, Hong Liu, Péter Pál Pach

Liu, Pach and Sándor recently characterized all polynomials $p (z)$ such that the equation $x + y = p (z)$ is $2$ -Ramsey, that is, any $2$ -coloring of $N$ contains infinitely ma…

math.CO2024

Extremal density for subdivisions with length or sparsity constraints

Jaehoon Kim, Hong Liu, Yantao Tang +3

Given a graph $H$ , a balanced subdivision of $H$ is obtained by replacing all edges of $H$ with internally disjoint paths of the same length. In this paper, we prove that for any g…