기초과학연구원 이산수학그룹
Given a graph, how do we construct a surface so that the graph embeds in that surface in an optimal way? Thomassen showed that for minimum genus as optimality criterion, …
A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all …
Many problems that are NP-hard in general become tractable on `structurally recursive’ graph classes. For example, consider classes of bounded tree- or clique-width. Since the 1990s, many directed analogues of …
A convex lattice polytope is the convex hull of a set of integral points. Vershik conjectured the existence of a limit shape for random convex lattice polygons, and three proofs …
Given a minor-closed graph class ${\cal G}$, the (minor) obstruction of ${\cal G}$ is the set of all minor-minimal graphs not in ${\cal G}$. Given a non-negative integer $k$, we define …
Let $\mathbb{F}_q$ be a finite field of order $q$ which is a prime power. In the finite field setting, we say that a function $\phi\colon \mathbb{F}_q^d\times \mathbb{F}_q^d\to \mathbb{F}_q$ is a Mattila-Sjölin …
Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, …
An intersection digraph is a digraph where every vertex $v$ is represented by an ordered pair $(S_v, T_v)$ of sets such that there is an edge from $v$ to $w$ …
An interval graph is the intersection graph of a family of intervals in the real line. Motivated by problems in ecology, Roberts defined the boxicity of a graph G to …
The preservation of symmetry is one of the key tools for designing data-efficient neural networks. A representative example is convolutional neural networks (CNNs); they preserve translation symmetries, and this symmetry …