Discrete Mathematics Group

2026 Workshop on Topological Combinatorics
2026-06-28 - 2026-07-11 | GIST
The 2026 Workshop on Topological Combinatorics will be held from June 28 to July 11, 2026 at Gwangju Institute of Science and Technology (GIST), located in Gwangju in the southwest of Republic of Korea.
The workshop aims to bring together researchers interested in applications of topology to combinatorics and related areas. This will be the fifth workshop in a series initiated by Ron Aharoni (August 2018 in Shantou, July 2019 in Prague, July 2020 on Zoom, and June 2024 in Paris).
The first week (June 28 – July 04) will be reserved for presentations, while the following days (July 05 – July 11) will be for discussion and collaborations.
The campus offers a variety of amenities, including a guesthouse that can accommodate approximately 20 guests.
In addition, various lodging options are available within a 15–20 minute walking distance.
We are planning to provide accommodation for all invited participants, and we are also considering offering partial travel support for those with limited funding.

Website: https://sites.google.com/view/2026topocomb

Ting-Wei Chao, The Oddtown Problem Modulo a Composite Number
2026-07-10 16:30 - 17:30 (Asia/Seoul) | Room B332, IBS (기초과학연구원)
A family of sets in $[n]$ is called an $ell$-Oddtown if the sizes of all sets are not divisible by $ell$, but the sizes of pairwise intersections are divisible by $ell$. The problem was completely solved when $ell$ is a prime via an elegant linear algebraic method, showing that the family has size at most $n$. However, not much was known for composite numbers. By splitting the family into families correspond to each prime factor of $ell$, one can show that the number is at most $omega n$, where $omega$ is the number of prime factors of $ell$. We used both combinatorial and Fourier analytic arguments to prove that the number of sets in any $ell$-Oddtown is at most $omega n-(2omega+varepsilon)log_2 n$ for most $n,ell$.

Yaobin Chen, Maximum in-general-position set in a random subset of $mathbb{F}^d_q$
2026-07-14 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Let $alpha(mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in a $p$-random subset of $mathbb{F}_q^d$. We determine the order of magnitude of $alpha(mathbb{F}_q^{d},p)$ up to a polylogarithmic factor by proving the balanced supersaturation conjecture of Balogh and Luo. Our result also resolves a conjecture implicitly posed by the first author, Liu, the second author and Zeng. In the course of our proof, we establish a lemma that demonstrates a “structure vs. randomness” phenomenon for point sets in finite-field linear spaces, which may be of independent interest.
This is joint work with Jiaxi Nie, Jing Yu, and Wentao Zhang.

Sang-il Oum (엄상일), A proof of the cycle double cover conjecture by OpenAI
2026-07-16 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
The cycle double cover conjecture (CDC) claims that every graph without cut-edges has a list of cycles such that every edge appears exactly twice in the list. This conjecture was proposed in 1970s by several mathematicians independently, including Tutte, Seymour, and Szekeres.
On July 10, 2026, OpenAI released a proof found by its ChatGPT 5.6 Sol Ultra. I will explain a slightly modified proof, with the aim of making it mostly accessible to undergraduate students.

Zichao Dong, $k$-wise odd-even towns
2026-07-21 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
For $boldsymbol{alpha} = (alpha_1, dots, alpha_k) in {mathbb F}_2^k$, an $boldsymbol{alpha} $-town is a set family in which every $i$-wise intersection has parity $alpha_i$. Denote by $f_{boldsymbol{alpha} }(n)$ the maximum size of an $boldsymbol{alpha} $-town on $[n]$. The classical oddtown and eventown problems study the cases $boldsymbol{alpha} = (1, 0)$ and $(0, 0)$, respectively. We determine the sharp asymptotics of $f_{boldsymbol{alpha} }(n)$ for all $boldsymbol{alpha} $, answering questions of Johnston-O’Neill and Wei-Zhang-Ge.

2026 Korean Student Combinatorics Workshop
2026-07-27 - 2026-07-31 | Gongju Hanok Village, Gongju
Website: https://kscw.combinatorics.kr/

Stephan Kreutzer, Disjoint Paths in Graphs and Digraphs
2026-07-28 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
One of the important algorithmic consequences of Robertson and Seymour’s Graph Minor Project is their proof that the k-Vertex-Disjoint Paths problem is fixed-parameter tractable on the class of all undirected graphs, that is, solvable in time $f(k) cdot n^c$, for some function $f$ and constant $c$.
For directed graphs the problem is significantly harder: the k-Disjoint-Paths problem it is NP-complete already for $k=2$. While this indicates that the Directed-k-Disjoint Paths problem is unlikely to be fixed-parameter tractable in general, it is nevertheless interesting to investigate which of the techniques used to solve the problem on undirected graphs fail for digraphs and why and whether some of them can be made to work in a more restricted setting.
In this talk I will speak about recent results on disjoint directed paths including positive solutions for special graph classes such as Eulerian digraphs but also recently obtained further hardness results.

Tomohiro Koana, A Single-Exponential FPT Algorithm for 2-Vertex-Connectivity Augmentation
2026-08-04 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
We study restricted-link augmentation to 2-vertex-connectivity. An instance consists of a graph $G$, possibly disconnected, a set $L$ of admissible links on its vertices, integer link costs in ${1, ldots, W}$, and an integer $k$; the task is to add at most $k$ links of minimum total cost so that the resulting multigraph is 2-vertex-connected. Recent work gives $O^*(k^{O(k)})$-time algorithms for unweighted λ-vertex-connectivity augmentation for every λ ≤ 4 [Carmesin and Ramanujan, SODA 2026], and an $O^*((k + λ)^{O(k)})$-time algorithm for arbitrary λ [Korhonen and Thorup, FOCS 2026]. We give a deterministic algorithm with running time $O^*(36^k W)$. Thus, for λ = 2, the unweighted running time improves from $O^*(k^{O(k)})$ to $O^*(36^k)$, and the algorithm also handles link costs with pseudo-polynomial dependence on $W$.
We reduce the problem to a boundary-pair variant of 2-vertex-connected spanning subgraph, where each vertex is assigned a pair of incident edges with an associated pair cost. We solve this variant using a cancellation identity, inspired by Cut&Count [Cygan et al., TALG 2022], obtained by applying Möbius inversion to decompositions along cut vertices: the identity cancels every connected spanning graph with more than one block and keeps exactly the 2-vertex-connected spanning graphs.

Meike Hatzel, Directed tree-cutwidth and immersions
2026-08-05 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
The first major step towards the graph minor structure theorem by Robertson and Seymour was the grid theorem, a result describing that every graph of large treewidth contains a grid as minor. In 2014 Wollan gave a definition for a tree-like decomposition and a width parameter tree-cutwidth with respect to immersions, a different graph containment relation. He provided results linking this parameter to immersions of large walls. This talk presents a version of this parameter for directed graphs, the directed tree-cutwidth. The main result is a grid theorem for directed tree-cutwidth establishing that it is linked to directed immersions of large cylindrical walls.
The presented work is joined with Marcin Briański, Karolina Okrasa, and Michał Pilipczuk.

2026 Summer School on Combinatorics and Algorithms (2026 조합론 및 알고리즘 여름학교)
2026-08-10 - 2026-08-14 | Bldg. E11, KAIST
The 2026 Summer School on Combinatorics and Algorithms is a venue for students and early-career researchers to learn selected topics in theoretical computer science and discrete mathematics. It will be a great opportunity for young and aspiring researchers to study topics which are important but not covered during the lectures in the university classes.
Website: https://combialgo.dimag.kr/2026/
Lecturers and Topics

Daniel Dadush, CWI, Amsterdam

Algorithms & Geometry of Linear Programming

Magnus Wahlström, Royal Holloway, University of London

Matroids, delta-matroids, and applications

Schedule

Start on 10 August 2026 Monday, 2 PM
End on 14 August 2025 Friday, 5 PM

Jinyoung Park (박진영), TBA
2026-08-18 16:30 - 17:30 | Room B332, IBS (기초과학연구원)

David Wood, TBA
2026-09-22 16:30 - 17:30 | Room B332, IBS (기초과학연구원)

2026 Combinatorics Workshop (2026 조합론 학술대회)
2026-10-20 - 2026-10-22 | Konjiam Resort, EW Village, B2, Meeting Room OPUS2
Combinatorics Workshop (조합론 학술대회) is an annual conference for researchers in combinatorics and related areas in Korea. It was started in 2004 by the Yonsei University BK21 Research Group. Since 2013, this workshop has been advised by the committee of discrete mathematics of the Korean Mathematical Society.
Website: https://cw2026.combinatorics.kr/en/
Venue
Konjiam Resort, EW Village, B2, Meeting Room OPUS2
(278, Docheogwit-Ro, Docheok-Myeon, Gwangju-Si, Gyeonggi-Do, Korea)

Travel Instructions

Dates
October 20 to 22, 2026
Plenary Speaker
Alexander V. Kostochka (UIUC)
Invited Speakers

Cheolwon Heo (SUNY Korea)
Tony Huynh (IBS DIMAG)
Dabeen Lee (Seoul National University)
Jongbaek Song (Pusan National University)

Contributed Talks
Each contributed talk will be about 20 minutes, including questions. Please note that we may stop accepting contributed talk applications before the deadline if all available slots are filled.
If you are interested in giving a contributed talk at the workshop, please submit an abstract by August 31, 2026.
To apply for a contributed talk, go to Call for Abstracts on Indico and click “Submit new abstract.” You may need to create an IBS Indico account.
Registration
Registration link
The registration deadline is August 31, 2026.
Organizing Committee

Ilkyoo Choi (최일규), Hankuk University of Foreign Studies, IBS Discrete Mathematics Group, KIAS
Sang-il Oum (엄상일), IBS Discrete Mathematics Group
Boram Park (박보람), Seoul National University

Advisory Committee
Committee of Discrete Mathematics, The Korean Mathematical Society (Chair: Sang-il Oum)
Sponsors

IBS Discrete Mathematics Group
Korean Mathematical Society
Seoul National University
Hankuk University of Foreign Studies
