기초과학연구원 이산수학그룹
Bouchet introduced isotropic systems in 1983 unifying some combinatorial features of binary matroids and 4-regular graphs. The concept of isotropic system is a useful tool to study vertex-minors of graphs …
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set …
A signed graph is a graph in which each edge has a positive or negative sign. Calling two graphs switch equivalent if one can get from one to the other …
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 …
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 …
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 …
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 $w$ …
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 …
In this talk, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations in terms of the …
For positive integers, $r \ge 3, h \ge 1,$ and $k \ge 1$, Bollobás, Saito, and Wormald proved some sufficient conditions for an $h$-edge-connected $r$-regular graph to have a k-factor …