Ilkyoo Choi

collaborators

8 papers

cs.LO2026

Lean-GAP: A Dataset of Formalized Graduate Algebra Problems

Seewoo Lee, Byung-Hak Hwang, Hyojae Lim +10

We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pi…

math.CO2026

Existence of cycles of length divisible by 3 or 4

Ilkyoo Choi, Hojin Chu, Ringi Kim +1

Dean conjectured that for each integer $k \geq 3$ , every graph with minimum degree at least $k$ has a cycle whose length is divisible by $k$ ; this conjecture is known to be true for…

math.CO2026

A lower bound on the number of edges in DP-critical graphs

Peter Bradshaw, Ilkyoo Choi, Alexandr Kostochka +1

A graph $G$ is $k$ -critical (list $k$ -critical, DP $k$ -critical) if $I ¨ (G) = k$ ( $I ¨ _{ℓ} (G) = k$ , $I ¨ _{DP} (G) = k$ ) and for every proper subgraph $G^{'}$ of $G$ , $I ¨ (G^{'}) < k$ ($Ï_…

math.CO2025

Flexible DP 3-coloring of sparse multigraphs

Peter Bradshaw, Ilkyoo Choi, Alexandr Kostochka

A \emph{request} on a graph assigns a preferred color to a subset of the vertices. A graph $G$ is \emph{ $I^µ$ -flexibly $k$ -choosable} if for every $k$ -list assignment $L$ and every…

math.CO2025

Between proper and square colorings of sparse graphs

Ilkyoo Choi, Xujun Liu

An $i$ -independent set is a set of vertices whose pairwise distance is at least $i + 1$ . A proper coloring (resp. a square coloring) of a graph is a partition of its vertices into in…

math.CO2025

On Alon-Tarsi orientations of sparse graphs

Eun-Kyung Cho, Ilkyoo Choi, Boram Park +1

Assume $G$ is a graph, $(v_{1}, \dots, v_{k})$ is a sequence of distinct vertices of $G$ , and $(a_{1}, \dots, a_{k})$ is an integer sequence with $a_{i} \in {1, 2}$ . We say $G$ is \emph{$(a_1…