Discrete Mathematics Group

Zichao Dong, $k$-wise odd-even towns
2026-07-21 16:30 - 17:30 (Asia/Seoul) | 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), A reformulation of Talagrand's Discrete Convexity Conjecture
2026-08-18 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
The “Convexity Conjecture” by Talagrand asks, roughly speaking, whether one can “create convexity” in a bounded number of steps regardless of the dimension of the ambient space. Talagrand also proposed a discrete version of this conjecture, calling it his “lifetime favorite problem” and offering a $1,000 prize for its solution. While the continuous version of the conjecture was recently proven by Hua, Song, and Tudose, the discrete analogue remains wide open. In this talk, we introduce a reformulation of the discrete convexity conjecture using the new notion of “k-thresholds,” an extension of the traditional definition of thresholds. Using this framework, we establish the conjecture for several special cases, focusing primarily on graph properties.

Ben Lund, TBA
2026-09-01 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
