기초과학연구원 이산수학그룹
Various types of independent sets have been studied for decades. As an example, the minimum number of maximal independent sets in a connected graph of given order is easy to …
The Graphic Travelling Salesman Problem is the problem of finding a spanning closed walk (a TSP walk) of minimum length in a given connected graph. The special case of the …
I will first introduce the notion of recognisability of languages of terms and then its extensions to sets of relational structures. In a second step, I will discuss relations with …
We introduce the notion of delineation. A graph class $\mathcal C$ is said delineated by twin-width (or simply, delineated) if for every hereditary closure $\mathcal D$ of a subclass of …
Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a given boolean predicate. A certificate …
The first course in graph theory usually covers concepts such as matchings, independent sets, colourings, and forbidden subgraphs. Around 2004, Borgs, Chayes, Lovász, Sós, Szegedy, and Vestergombi introduced a very …
The Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on n vertices is at most n. In this talk, I will sketch a proof …
We show that there is no $2^{o(k^2)} n^{O(1)}$ time algorithm for Independent Set on $n$-vertex graphs with rank-width $k$, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches …
Hadwiger's famous coloring conjecture states that every t-chromatic graph contains a $K_t$-minor. Holroyd conjectured the following strengthening of Hadwiger's conjecture: If G is a t-chromatic graph and S⊆V(G) takes all …
A circle graph is an intersection graph of a set of chords of a circle. In this talk, I will describe the unavoidable induced subgraphs of circle graphs with large …