Jinha Kim (김진하), Independent domination of graphs with bounded maximum degree
Room B232 IBS (기초과학연구원)An independent dominating set of a graph, also known as a maximal independent set, is a set
An independent dominating set of a graph, also known as a maximal independent set, is a set
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 distance between u and v in T is at most k. The graph classes of k-leaf powers have several applications in computational biology, but recognizing …
Tutte (1961) proved that every simple
Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field
This talk follows on from the recent talk of Pascal Gollin in this seminar series, but will aim to be accessible for newcomers. Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. By …
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, is either Hamiltonian or contains a cycle of length at least 2d. Second, the theorem of Erdős-Gallai from 1959, states that a 2-connected graph G …
It is known that the rank- and tree-width of the random graph
This program consists of a short intensive workshop, where mathematicians from across the globe will come together to work on open problems in structural graph theory. We will consider the following research themes: graph minors, graph colouring, Hadwiger’s Conjecture, bounded expansion classes, graph product structure theory, generalised colouring numbers, VC dimension, induced subgraphs, Erdős-Hajnal conjecture, …
The Ramsey number
Suppose that