Donggyu Kim

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5 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

Graphs whose Eulerian trails have unique labels

Donggyu Kim, Rose McCarty, Caleb McFarland

Consider an undirected graph whose edges are labeled invertibly in a group. When does every Eulerian trail from one fixed vertex to another have the same label? We give a precise s…

math.CO2026

Pseudo-orientable ribbon graphs: Matrix--Quasi-tree Theorem and log-concavity

Changxin Ding, Donggyu Kim

One of the most important classes of even $Δ$ -matroids arises from orientable ribbon graphs, which play a role analogous to that of graphic matroids in matroid theory. Motivated by…

math.CO2025

Turán's theorem for Dowling geometries

Rutger Campbell, Donggyu Kim, Jorn van der Pol

The Dowling geometry $Q_{n} (Γ)$ , where $Γ$ is a finite group, is a matroid that generalizes the complete-graphic matroid $M (K_{n + 1})$ . We determine the maximum size of an $N$ -free su…

math.CO2025

Reconstructing hypergraph matching polynomials

Donggyu Kim, Hyunwoo Lee

By utilizing the recently developed hypergraph analogue of Godsil's identity by the second author, we prove that for all $n \geq k \geq 2$ , one can reconstruct the matching polynom…