기초과학연구원 이산수학그룹
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 …
For each integer $k\ge 2$, we determine a sharp bound on $\operatorname{mad}(G)$ such that $V(G)$ can be partitioned into sets $I$ and $F_k$, where $I$ is an independent set and $G$ …
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 …
In this talk I will present a small result we achieved during a workshop in February this year. My coauthors on this are Marcin Pilipczuk, Paweł Komosa and Manuel Sorge. A …
Shrub-depth is a graph invariant often considered as an extension of tree-depth to dense graphs. In this talk I will explain our recent proofs of two results about graphs of …
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 …
In extremal graph theory, a graph G is H-saturated if G does not contain a copy of H but adding any missing edge to G creates a copy of H. …
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 …
There has been much research on finding a large rainbow matching in a properly edge-colored graph, where a proper edge coloring is a coloring of the edge set such that …
A graph $H$ is common if the number of monochromatic copies of $H$ in a 2-edge-colouring of the complete graph $K_n$ is minimised by the random colouring. Burr and Rosta, extending …