Seokbeom Kim

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math.CO2026

Every tournament of dichromatic number $10 k^{2}$ has a vertex whose out-neighborhood has dichromatic number more than $k$

Seokbeom Kim, Sang-il Oum

The dichromatic number of a tournament is the minimum number of colors needed to color the vertices so that no directed cycle is monochromatic. Nguyen, Scott, and Seymour (2025) as…

math.CO2026

On the chromatic number of the union of comparability graphs

Wouter Cames van Batenburg, Maria Chudnovsky, Linda Cook +3

Resolving in a strong sense a problem of Gyárfás on the union of two perfect graphs, we prove that for every pair of positive integers $d$ and $k$ , there is a graph $G$ with clique…

math.CO2026

On a weaker notion of cross $t$ -intersecting families

Jiangdong Ai, Ming Chen, Seokbeom Kim +1

We prove that if two families $F \subseteq (k [ n ])$ and $F^{'} \subseteq (k ^{'} [ n ])$ satisfy $\sum_{1 \leq i, j \leq \ell} \lvert F_i \cap F_j' \rvert…

Every tournament of dichromatic number 10k2 has a vertex whose out-neighborhood has dichromatic number more than k

On the chromatic number of the union of comparability graphs

On a weaker notion of cross t-intersecting families

Every tournament of dichromatic number $10 k^{2}$ has a vertex whose out-neighborhood has dichromatic number more than $k$

On a weaker notion of cross $t$ -intersecting families