Casey Tompkins, Extremal forbidden poset problems in Boolean and linear lattices

Room B232 IBS (기초과학연구원)

Extending the classical theorem of Sperner on the maximum size of an antichain in the Boolean lattice, Katona and Tarján introduced a general extremal function $La(n,P)$, defined to be the maximum size of a family of subsets of $$ which does not contain a given poset $P$ among its containment relations.  In this talk, I

Meike Hatzel, Constant congestion bramble

Zoom ID: 869 4632 6610 (ibsdimag)

In this talk I will present a small result we achieved during a workshop in February this year. My coauthors on this are Marcin Pilipczuk, Paweł Komosa and Manuel Sorge. A bramble in an undirected graph $G$ is a family of connected subgraphs of $G$ such that for every two subgraphs $H_1$ and $H_2$ in the bramble either $V(H_1) \cap

Yijia Chen (陈翌佳), Graphs of bounded shrub-depth, through a logic lens

Zoom ID: 869 4632 6610 (ibsdimag)

Shrub-depth is a graph invariant often considered as an extension of tree-depth to dense graphs. In this talk I will explain our recent proofs of two results about graphs of bounded shrub-depth. Every graph property definable in monadic-second order logic, e.g., 3-colorability, can be evaluated by Boolean circuits of constant depth and polynomial size, whose

Duksang Lee (이덕상), Characterizing matroids whose bases form graphic delta-matroids

Room B232 IBS (기초과학연구원)

We introduce delta-graphic matroids, which are matroids whose bases form graphic delta-matroids. The class of delta-graphic matroids contains graphic matroids as well as cographic matroids and is a proper subclass of the class of regular matroids. We give a structural characterization of the class of delta-graphic matroids. We also show that every forbidden minor for

Da Qi Chen, Bipartite Saturation

Zoom ID: 869 4632 6610 (ibsdimag)

In extremal graph theory, a graph G is H-saturated if G does not contain a copy of H but adding any missing edge to G creates a copy of H. The saturation number, sat(n, H), is the minimum number of edges in an n-vertex H-saturated graph. This class of problems was first studied by Zykov

Livestream

Joonkyung Lee (이준경), On Ramsey multiplicity

Zoom ID:8628398170 (123450)

Ramsey's theorem states that, for a fixed graph $H$, every 2-edge-colouring of $K_n$ contains a monochromatic copy of $H$ whenever $n$ is large enough. Perhaps one of the most natural questions after Ramsey's theorem is then how many copies of monochromatic $H$ can be guaranteed to exist. To formalise this question, let the Ramsey multiplicity

Debsoumya Chakraborti, Rainbow matchings in edge-colored simple graphs

Room B232 IBS (기초과학연구원)

There has been much research on finding a large rainbow matching in a properly edge-colored graph, where a proper edge coloring is a coloring of the edge set such that no same-colored edges are incident. Barát, Gyárfás, and Sárközy conjectured that in every proper edge coloring of a multigraph (with parallel edges allowed, but not

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: 869 4632 6610 (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

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