Seonghyuk Im

activity

20182026

collaborators

Showing math.COShow all

14 papers · 1 filter

math.CO2026

On the enumeration of polymatroids

Seonghyuk Im, Donggyu Kim

Let $p_{k} (n)$ be the number of $k$ -polymatroids on $[n]$ . We show that for every fixed $k \geq 1$ , we have \[ \left\lfloor \frac{k}{2} \right\rfloor \cdot \binom{n}{\lfloor n/2 \rfl…

math.CO2026

Note on the codegree version of the Erdős--Ko--Rado theorem

Luyining Gan, Jie Han, Seonghyuk Im

Kupavskii proved a codegree version of the Erdős--Ko--Rado theorem by showing that for an intersecting family $F \subseteq (k [ n ])$ with $n \geq 2 k + 3 d / (1 - d / k)$ , t…

math.CO2026

Hitting time for Hamilton cycles in pseudorandom graphs

Yaobin Chen, Yu Chen, Seonghyuk Im +1

Consider the random subgraph process on a base graph $G$ with $n$ vertices: we generate a sequence ${G_{t}}_{t = 0}^{∣ E (G) ∣}$ by taking a uniformly random ordering of the edges of $G…

math.CO2026

The perturbation threshold of degenerate graphs

Jie Han, Seonghyuk Im, Bin Wang +1

We show that for any $d \geq 2$ and $Δ > 0$ there exists $η > 0$ such that the following holds: Let $G$ be an $n$ -vertex graph with at least $Ω (n^{2})$ edges and let $H$ be an $n$ -vertex $…

math.CO2025

Berge Hamilton cycles in a random sparsification of dense hypergraphs

Seonghyuk Im, Minseo Kim

In the standard random graph process, edges are added to an initially empty graph one by one uniformly at random. A classic result by Ajtai, Komlós, and Szemerédi, and independentl…

math.CO2025

Perturbation of dense graphs

Jie Han, Seonghyuk Im, Bin Wang +1

In the past two decades, various properties of randomly perturbed/augmented (hyper)graphs have been intensively studied, since the model was introduced by Bohman, Frieze and Martin…