기초과학연구원 이산수학그룹
Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices, and it extends also to other binary relational structures, e.g. to digraphs and posets. It was introduced …
The Alon-Jaeger-Tarsi conjecture states that for any finite field $\mathbb{F}$ of size at least 4 and any nonsingular matrix $M$ over $\mathbb{F}$ there exists a vector $x$ such that neither …
The Gyárfás-Sumner conjecture says that for every forest $H$, there is a function $f$ such that the chromatic number $\chi(G)$ is at most $f(\omega(G))$ for every $H$-free graph $G$ ("$H$-free" means with …
The independence number of a tree decomposition $\mathcal{T}$ of a graph is the smallest integer $k$ such that each bag of $\mathcal{T}$ induces a subgraph with independence number at most …
Matching minors are a specialisation of minors which preserves the existence and elementary structural properties of perfect matchings. They were first discovered as part of the study of the Pfaffian …
Branchwidth determines how graphs, and more generally, arbitrary connectivity (basically symmetric and submodular) functions could be decomposed into a tree-like structure by specific cuts. We develop a general framework for …
I will discuss various results for rainbow matching problems. In particular, I will introduce a ‘sampling trick’ which can be used to obtain short proofs of old results as well …
The Caccetta-Haggkvist conjecture, one of the best known in graph theory, is that in a digraph with $n$ vertices in which all outdegrees are at least $n/k$ there is a …
Graph Minor project by Robertson and Seymour is perhaps the deepest theory in Graph Theory. It gives a deep structural characterization of graphs without any graph $H$ as a minor. …
Our talk will mainly focus on the relationship between substructures and eigenvalues of graphs. We will briefly survey recent developments on a conjecture of Bollobás and Nikiforov and a classical …