Seonghyuk Im

activity

20242026

collaborators

11 papers

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 ErdÅs--Ko--Rado theorem

Luyining Gan, Jie Han, Seonghyuk Im

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

math.CO2026

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, KomlÃ³s, and SzemerÃ©di, and independen…

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 $I^ > 0$ there exists $I^\cdot > 0$ such that the following holds: Let $G$ be an $n$ -vertex graph with at least $I^c ◯ (n^{2})$ edges and let $H$ be an $n$ -verte…

cs.DM2025

An efficient algorithm for $F$ -subgraph-free Edge Deletion on graphs having a product structure

Shinwoo An, Seonghyuk Im, Seokbeom Kim +1

Given a family $F$ of graphs, a graph is \emph{ $F$ -subgraph-free} if it has no subgraph isomorphic to a member of $F$ . We present a fixed-parameter li…

On the enumeration of polymatroids

Note on the codegree version of the ErdÅs--Ko--Rado theorem

Berge Hamilton cycles in a random sparsification of dense hypergraphs

Hitting time for Hamilton cycles in pseudorandom graphs

The perturbation threshold of degenerate graphs

An efficient algorithm for F-subgraph-free Edge Deletion on graphs having a product structure

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

An efficient algorithm for $F$ -subgraph-free Edge Deletion on graphs having a product structure