Livestream

### Joonkyung Lee (이준경), On common graphs

Zoom ID:8628398170 (123450)

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 a famous conjecture by Erdős, conjectured that every graph is common. The conjectures by Erdős and by Burr and Rosta were disproved by Thomason and

### Deniz Sarikaya, What means Hamiltonicity for infinite graphs and how to force it via forbidden induced subgraphs

Zoom ID: 934 3222 0374 (ibsdimag)

The study of Hamiltonian graphs, i.e. finite graphs having a cycle that contains all vertices of the graph, is a central theme of finite graph theory. For infinite graphs such a definition cannot work, since cycles are finite. We shall debate possible concepts of Hamiltonicity for infinite graphs and eventually follow the topological approach by

### Hong Liu (刘鸿), A solution to Erdős and Hajnal’s odd cycle problem

Room B232 IBS (기초과학연구원)

I will go over the history on the study of the set of cycle lengths of graphs with large average degree or chromatic number, and discuss recent work with Richard Montgomery on this topic. In particular, we will see the divergence of harmonic sum of odd cycle lengths in graphs with large chromatic number and

### Karl Heuer, Even Circuits in Oriented Matroids

Zoom ID: 934 3222 0374 (ibsdimag)

In this talk I will state a generalisation of the even directed cycle problem, which asks whether a given digraph contains a directed cycle of even length, to orientations of regular matroids. Motivated by this problem, I will define non-even oriented matroids generalising non-even digraphs, which played a central role in resolving the computational complexity of

### Jaiung Jun (전재웅), On the Hopf algebra of multi-complexes

Zoom ID: 934 3222 0374 (ibsdimag)

In combinatorics, Hopf algebras appear naturally when studying various classes of combinatorial objects, such as graphs, matroids, posets or symmetric functions. Given such a class of combinatorial objects, basic information on these objects regarding assembly and disassembly operations are encoded in the algebraic structure of a Hopf algebra. One then hopes to use algebraic identities of

### Jinha Kim (김진하), On a conjecture by Kalai and Meshulam – the Betti number of the independence complex of ternary graphs

Room B232 IBS (기초과학연구원)

Given a graph G=(V,E), the independence complex of G is the abstract simplicial complex I(G) on V whose faces are the independent sets of G. A graph is ternary if it does not contain an induced cycle of length divisible by three. Kalai and Meshulam conjectured that if G is ternary then the sum of the Betti numbers

### Paul Seymour, The Erdős-Hajnal conjecture is true for excluding a five-cycle

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In an n-vertex graph, there must be a clique or stable set of size at least $C\log n$, and there are graphs where this bound is attained. But if we look at graphs not containing a fixed graph H as an induced subgraph, the largest clique or stable set is bigger. Erdős and Hajnal conjectured in 1977 that

### O-joung Kwon (권오정), Directed tangles and applications

Room B232 IBS (기초과학연구원)

The canonical tree-decomposition theorem, proved by Robertson and Seymour in their seminal graph minors series, turns out to be an extremely valuable tool in structural and algorithmic graph theory. In this paper, we prove the analogous result for digraphs, the directed tangle tree-decomposition theorem. More precisely, we introduce directed tangles and provide a directed tree-decomposition

### Andreas Holmsen, Discrete geometry in convexity spaces

Room B232 IBS (기초과학연구원)

The notion of convexity spaces provides a purely combinatorial framework for certain problems in discrete geometry. In the last ten years, we have seen some progress on several open problems in the area, and in this talk, I will focus on the recent results relating to Tverberg’s theorem and the Alon-Kleitman (p,q) theorem.

### Rose McCarty, Vertex-minors and flooding immersions

Zoom ID: 934 3222 0374 (ibsdimag)

An immersion of a graph H into a graph G sends edges of H into edge-disjoint trails of G. We say the immersion is flooding if every edge of G is in one of the trails. Flooding immersions are interesting for Eulerian group-labelled graphs; in this context they behave quite differently from regular immersions. Moreover,

기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209