Seunghun Lee

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math.CO2025

On an extension problem on the moment curve

Seunghun Lee, Eran Nevo

We show that for $2 \leq d \leq 4$ , every finite geometric simplicial complex $Δ$ in $R^{d}$ with vertices on the moment curve can be extended to a triangulation $T$ of the cycl…

math.CO2025

Colorful circuits and colorful topes in oriented matroids

Minho Cho, Seunghun Lee, Frédéric Meunier

We provide a short proof of a conic version of the colorful Carathéodory theorem for oriented matroids. Holmsen's extension of the colorful Carathéodory theorem to oriented matroid…

math.CO2024

The interval coloring impropriety of planar graphs

Seunghun Lee

For a graph $G$ , we call an edge coloring of $G$ an \textit{improper} \textit{interval edge coloring} if for every $v \in V (G)$ the colors, which are integers, of the edges incident…

math.CO2024

On conflict-free colorings of cyclic polytopes and the girth conjecture for graphs

Seunghun Lee, Shakhar Smorodinsky

We study the conflict-free chromatic number of hypergraphs derived from the family of facets of $d$ -dimensional cyclic polytopes with $n$ vertices. While in odd dimensions $d$ the…