기초과학연구원 이산수학그룹
Let E be a finite set and I be a collection of subsets of E. When is there a set of real vectors indexed by E such that I correspond to its linearly independent subsets? In 1935, …
Generalized extremal problems have been one of the central topics of study in extremal combinatorics throughout the last few decades. One such simple-looking problem, maximizing the number of cliques of …
Let $G$ be a graph on the vertex set $V$. A vertex subset $W \subset V$ is a cover of $G$ if $V \setminus W$ is an independent set of …
Let $G$ be a graph on $V$ and $n$ a positive integer. Let $I_n(G)$ be the abstract simplicial complex whose faces are the subsets of $V$ that do not contain …
For any given graph $H$, one may define a natural corresponding functional $\|.\|_H$ for real-valued functions by using homomorphism density. One may also extend this to complex-valued functions, once $H$ …
We introduce some of well-known game-theoretic graph models and related problems. A contagion game model explains how an innovation diffuses over a given network structure and focuses on finding conditions …
Whitney’s 2-Isomorphism Theorem characterises when two graphs have isomorphic cycle matroids. In this talk, we present an analogue of this theorem for graphs embedded in surfaces by characterising when two …
Extending the classical theorem of Sperner on the maximum size of an antichain in the Boolean lattice, Katona and Tarján introduced a general extremal function $La(n,P)$, defined to be the …
We introduce delta-graphic matroids, which are matroids whose bases form graphic delta-matroids. The class of delta-graphic matroids contains graphic matroids as well as cographic matroids and is a proper subclass …
Ramsey's theorem states that, for a fixed graph $H$, every 2-edge-colouring of $K_n$ contains a monochromatic copy of $H$ whenever $n$ is large enough. Perhaps one of the most natural …