기초과학연구원 이산수학그룹
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: …
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 …
Let $P$ be a set of points in $PG(n+d,q)$, and let $L$ be a set of $n$-flats. Here, $n$-flat is a short name for $n$-dimensional projective subspaces. A classical bound of Haemers, rediscovered in an influential paper of Vinh, gives an upper bound on the difference between the number of incidences between $P$ and $L$ …
We introduce the concept of the saturation of a (bi)graph: the union closure after inductively adding its virtual elements, which are weighted ε-good (respectively ε-excellent sets) as in the Stable Regularity Lemma. In the Littlestone class and stable graph case, we show that if the saturation has bounded Littlestone dimension, then it is the smallest …
I discuss 'almost counterexamples' to Seymour's second neighbourhood conjecture. In what we call Seymour-tight orientations, the size of the first neighbourhood of each vertex equals the size of its second neighbourhood. We give several examples and constructions. Specifically, we prove that the class of Seymour-tight orientations is closed under taking (generalized) lexicographic products. Moreover, the …
We present an exposition of a proof, discovered by GPT-6 Astra, of the Erdős-Sós Conjecture, which states that every graph with average degree greater than t−2 contains every tree on t≥2 vertices.
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 …
A celebrated result of Bayer and Stillman from 1987 states that for a homogeneous ideal $I$ of a polynomial ring $S$, the regularities of $S/I$ and $S/\textrm{GIN}(I)$ are the same under the reverse lexicographic monomial ordering, where $\textrm{GIN}(I)$ is the generic initial ideal. If $R$ is a polynomial ring whose variables are subdivided into disjoint …
Treewidth is a graph parameter commonly used to quantify how "close" a graph is to a tree. Although it is a cornerstone of structural graph theory and algorithm design, it is nearly useless for algorithmic purposes in many dense graph classes. In this talk, we discuss the tree-independence number, a more versatile graph parameter that …
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, …