Meike Hatzel, Directed tree-cutwidth and immersions
2026-08-05 16:30 - 17:30 (Asia/Seoul) | 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.

Hyunwoo Lee (이현우), A super-exponential lower bound construction for the multicolor triangle Ramsey problem discovered by OpenAI
2026-08-07 15:00 - 16:00 | Room B332, IBS (기초과학연구원)
Let $R_k(3)$ denote the smallest integer $N$ such that every $k$-edge-coloring of the complete graph $K_N$ contains a monochromatic triangle. A simple inductive argument gives the classical factorial upper bound $R_k(3)leq k!=k^{O(k)}$, whereas the best previously known lower bound was only exponential in $k$, namely, $R_k(3)geq 2^{Omega(k)}$. It was a longstanding open problem of ErdH{o}s whether $R_k(3)$ grows exponentially or super-exponentially in $k$.
On August 1, 2026, OpenAI, using an internal AI model, discovered a construction establishing the super-exponential lower bound $R_k(3)geq k^{Omega(k)}$, thereby resolving Erdős’ longstanding question. In this talk, I will explain the construction and discuss possible directions for further research, some of which may already have been explored by other researchers.

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, Proof of the Clustered Hadwiger Conjecture
2026-09-22 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Hadwiger famously conjectured that every $K_h$-minor-free graph is properly $(h-1)$-colourable. This talk will present the following improper analogue of Hadwiger’s Conjecture: for fixed $h$, every $K_h$-minor-free graph is $(h-1)$-colourable with monochromatic components of bounded size. The number of colours is best possible regardless of the size of monochromatic components. This solves an open problem of Edwards, Kang, Kim, Oum and Seymour [SIAM J. Disc. Math. 2015], and concludes a line of research initiated in 2007. Similarly, for fixed $tgeqslant s$, we show that every $K_{s,t}$-minor-free graph is $(s+1)$-colourable with monochromatic components of bounded size. The number of colours is best possible, solving an open problem of van de Heuvel and Wood [J. London Math. Soc. 2018]. We actually prove a single theorem from which both of the above results are immediate corollaries. For an excluded apex minor, the result is strengthened as follows: for fixed $t geqslant s geqslant 3$, and for any fixed apex graph $X$, every $K_{s,t}$-subgraph-free $X$-minor-free graph is $(s+1)$-colourable with monochromatic components of bounded size. The number of colours is again best possible. This is joint work with Vida Dujmović, Louis Esperet and Pat Morin [arXiv:2306.06224].

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
