기초과학연구원 이산수학그룹
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 …
We prove that there is a function $f : \mathbb{N} \to \mathbb{N}$ such that for every function $g : \mathbb{N} \to \mathbb{N} \cup \{\infty\}$ with $g(1)=1$ and $g \ge f$, …
A graph G is a k-leaf power if there exists a tree T whose leaf set is V(G), and such that uv is an edge if and only if the …
We examine algorithmic extensions of two classic results of extremal combinatorics. First, the theorem of Dirac from 1952 asserts that a 2-connected graph G with the minimum vertex degree d>1, …
In 1982 Galvin, Rival, and Sands proved that in $K_{t,t}$-subgraph free graphs (t being fixed), the existence of a path of order n guarantees the existence of an induced path …
The first-order model checking problem for finite graphs asks, given a graph G and a first-order sentence $\phi$ as input, to decide whether $\phi$ holds on G. Showing the existence …
We prove that for every graph F with at least one edge there are graphs H of arbitrarily large chromatic number and the same clique number as F such that …