Mathematical Interests
Graph & Matroid Theory, Algebraic Combinatorics:
Graphs with vertex-/pivot-minors, (Delta-)matroids, Chip-firing games, Linear algebraic techniques in combinatorics, etc.
Affiliation
School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA
Preprints
11. Reconstructing hypergraph matching polynomials (with Hyunwoo Lee), arXiv: 2501.19081, 2025.
We prove that the matching polynomial of a k-uniform hypergraph H (each coefficient = # i-matchings) is reconstructible from the multi-set of induced subhypergraphs of order ~ (k/k-1)|H|, which generalizes Godsil’s theorem. This result is even more surprising when compared to Kocay’s result; hypergraphs are not reconstructible. It is proved by adapting linear algebraic techniques, and we also show the given bound is tight.
10. The Jacobian of a regular orthogonal matroid and torsor structures on spanning quasi-trees of ribbon graphs (with Matthew Baker and Changxin Ding), arXiv: 2501.08796, 2025.
We show that the set of spanning quasi-trees of a ribbon graph inherits a group structure of its Jacobian group (which first introduced by Merino, Moffatt, and Noble) without the distinguished identity element. It extends the same results for plane graphs by Chan–Church–Grochow and Baker–Wang, casting light on the role of embeddings of graphs.
A generalized Farkas Lemma for oriented orthogonal matroid is proved and used as a key lemma. It follows from the signed circuit axiom of oriented orthogonal matroids, as established in “Orthogonal matroids over tracts.”
9. Orthogonal matroids over tracts (with Tong Jin), arXiv: 2303.05353, 2023.
We extend theory of matroids with coefficients, introduced by Dress and Wenzel and developed by Baker and Bowler, to orthogonal matroids (= even delta-matroids). Orthogonal matroids are combinatorial data related to (orientable) ribbon graphs and orthogonal Grassmannian OGr(n,2n).
Accepted Papers
8. Baker-Bowler theory for Lagrangian Grassmannians, accepted in Int. Math. Res. Not. IMRN, arXiv: 2403.02356, 2024.
This is a sequel of the paper “Orthogonal matroids over tracts.” We define a new combinatorial object, named antisymmetric matroids, which captures common properties of (non-orientable) ribbon graphs and symplectic Grassmannian SpGr(n,2n), and develop theory of antisymmetric matroids with coefficients. Also, antisymmetric matroids are closely related with delta-matroids and gaussoids.
* At first, I named it a sympletic matroid, but since this name was already used in Coxeter matroid theory, I decided to name it antisymmetric matroid instead.
7. Note on Hamiltonicity of basis graphs of even delta-matroids (with Sang-il Oum), J. Graph Theory, March 2025. DOI: 10.1002/jgt.23237, arXiv: 2308.05772.
6. Twin-width of random graphs (with Jungho Ahn, Debsoumya Chakraborti, Kevin Hendrey, and Sang-il Oum), Random Structures Algorithms, June 2024. DOI: 10.1002/rsa.21247, arXiv: 2212.07880.
5. Vertex-minors of graphs: A survey (with Sang-il Oum), Discrete Appl. Math., July 2024. DOI: 10.1016/j.dam.2024.03.011.
4. Prime vertex-minors of a prime graph (with Sang-il Oum), European J. Combin., 118:103871, May 2024. DOI: 10.1016/j.ejc.2023.103871, arXiv: 2202:07877.
3. Eigenvalues and parity factors in graphs with given minimum degree, (with Suil O), Discrete Math., 346(4):113290, April 2023. DOI: 10.1016/j.disc.2022.113290, arXiv: 2111.12966.
2. Bounds for the Twin-width of Graphs (with Jungho Ahn, Kevin Hendrey, and Sang-il Oum), SIAM J. Discrete Math., 36(3):2352-2366, 2022. DOI: 10.1137/21M1452834, arXiv: 2110.03957.
1. Γ-graphic delta-matroids and their applications (with Duksang Lee and Sang-il Oum), In the Proceedings of the 32nd International Symposium on Algorithms and Computation (ISAAC2021, December 6-8, 2021, Fukuoka, Japan), Article No. 70; pp. 70:1-70:13, 2021. DOI: 10.4230/LIPIcs.ISAAC.2021.70. Combinatorica, 43(5):963-983, October 2023. DOI: 10.1007/s00493-023-00043-6, arXiv: 2104.11383.
List of Co-authors (# papers w/ me)
Jungho Ahn (2), Matthew Baker (1), Debsoumya Chakraborti (1), Changxin Ding (1), Kevin Hendrey (2), Tong Jin (1), Duksang Lee (1), Hyunwoo Lee (1), Suil O (1), Sang-il Oum (6)
Talks
Torsor structures on spanning quasi-trees of ribbon graphs – the Discrete Analysis Seminar (February 28, Yonsei University, Seoul, South Korea).
Baker-Bowler theory for Lagrangian Grassmannians – the Geometry of Matroids Workshop (October 21-25, IAS, Princeton, New Jersey, U.S.). (YouTube link)
Two ways to generalize matroids with coefficients – the 2024 Combinatorics Workshop (August 28-30, Chung Buk National University, Cheongju, South Korea).
Baker-Bowler theory for Lagrangian Grassmannians – the 2024 Workshop on (Mostly) Matroids (August 19-23, 2024, IBS, Daejeon, South Korea).
Baker-Bowler theory for Lagrangian Grassmannians – the SIAM Conference on Discrete Mathematics (DM24) (July 08-11, 2024, Spokane, Washington, U.S.).
Baker-Bowler theory for Lagrangian Grassmannians (Slides) – the 2024 KMS Spring Meeting (April 18-20, 2024, Daejeon, South Korea).
Baker-Bowler theory for Lagrangian Grassmannians – Joint seminar Atlanta-Groningen (April 15, 2024, Online).
Twin-width of random graphs – Combinatorics Seminar in Yeungnam University (March 18, 2024, Gyeongsan, Gyeongbuk, South Korea).
Orthogonal matroids over tracts (Slides) – presented at the 30th KIAS Combinatorics Workshop (March 08-09, 2024, Seoul, South Korea).
Hamiltonicity of basis graphs of even delta-matroids – presented at the 2023 KMS Annual Meeting (October 26-28, 2023, Seoul, South Korea).
Orthogonal matroids over tracts – presented in Discrete Math Seminar at IBS Discrete Mathematics Group (September 19, 2023, South Korea). (YouTube link)
Prime vertex-minors of prime graphs – presented at the CanaDAM 2023 (June 05-08, 2023, Winnipeg, Manitoba, Canada).
Orthogonal matroids over tracts – presented at the 2023 KMS Spring Meeting (April 27-29, 2023, Daejeon, South Korea).
(Poster) Orthogonal Matroids over Tracts – presented at the IBS ECOPRO and DIMAG poster day (Internal event, only poster, April 2022).
Matroid theory arising from projective geometry – presented at the Workshop for Young Mathematicians in Korea 2022 (Dec 03-04, 2022, KAIST, Daejeon, South Korea).
Stronger versions of Tutte’s wheel theorem for vertex-/pivot-minors -presented at the Student Symposium in Combinatorics 2022 (May 30-June 03, 2022, Australia).
(Poster) Γ-graphic delta-matroids and their applications – presented at the 2022 KSIAM Spring Conference (May 27-29, 2022, IBS, Daejeon, South Korea).
A stronger version of Tutte’s wheel theorem for vertex-minors -presented at the 2022 KMS Spring Meeting (April 28-29, 2022, South Korea).
A stronger version of Tutte’s wheel theorem for vertex-minors -presented in Discrete Math Seminar at IBS Discrete Mathematics Group (Feb 21, 2022, South Korea). (YouTube link)
Eigenvalues and parity factors in graphs
-presented in KAIST Math Graduate student Seminar (November 25, 2021, KAIST, South Korea).
Eigenvalues and parity factors in graphs
-presented in 2021 China-Korea Young Scholars’ Symposium on Discrete Mathematics, Statistics and Optimization (November 13-14, 2021, South Korea and China).
Γ-graphic delta-matroids and their applications
-presented in Discrete Math Seminar at IBS Discrete Mathematics Group (October 26, 2021, South Korea). (YouTube link)
Γ-graphic delta-matroids and their applications
-presented at the 2021 KMS Annual Meeting (October 20-22, 2021, South Korea).
Awards
Excellent Poster Award (Title: Γ-graphic delta-matroids and their applications), 2022 KSIAM Spring Conference.
Academic Services
Co-organizing 2024 Korean Student Combinatorics Workshop (July 29-August 02, 2024, Gongju, South Korea).
Contact info.
Homepage: https://dimag.ibs.re.kr/home/donggyu/
E-mail: donggyu@gatech.edu
(Old e-mail: donggyu@kaist.ac.kr )
Address: Skiles 237b,
School of Mathematics,
Georgia Institute of Technology,
686 Cherry Street,
Atlanta, GA 30332-0160 USA
CV
Miscellaneous
KAIST 45th Anniversary Emblem Contest – Prize winner (Jan. 6th, 2016)
KAIST Dept. of Mathematical Sciences Logo Design Contest – 2nd award (Nov. 29th, 2021)
My hobbies are cycling and hiking. Look at my best efforts!
(Cycling: https://www.strava.com/activities/7898025289)
(Hiking: https://www.strava.com/activities/7332013385)
(Running: https://www.strava.com/activities/10975901771)