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  • MATRIX-IBS Workshop: Structural Graph Theory Downunder III

    MATRIX, Australia

    Website: https://www.matrix-inst.org.au/events/structural-graph-theory-downunder-iii/ Program Description:  This program, jointly organised by MATRIX and the Discrete Mathematics Group of the Korean Institute for Basic Science (IBS), builds on the “Structural Graph Theory Downunder” programs held at MATRIX in 2019 and 2022. In this short intensive workshop, mathematicians from across the globe will come together to work on open …

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  • Shin-ichiro Seki, On the extension of the Green-Tao theorem to number fields

    Zoom ID: 897 6822 0619 (ibsecopro) [04/19 only]

    In 2006, Tao established the Gaussian counterpart of the celebrated Green-Tao theorem on arithmetic progressions of primes. In this talk, I will explain the extension of Tao's theorem and the Green-Tao theorem to the case of general number fields. Our combinatorial tool is the relative hypergraph removal lemma by Conlon-Fox-Zhao. I will discuss the difficulties …

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  • Hyunwoo Lee (이현우), On perfect subdivision tilings

    Room B332 IBS (기초과학연구원)

    For a given graph $H$, we say that a graph $G$ has a perfect $H$-subdivision tiling if $G$ contains a collection of vertex-disjoint subdivisions of $H$ covering all vertices of $G.$ Let $\delta_{sub}(n, H)$ be the smallest integer $k$ such that any $n$-vertex graph $G$ with minimum degree at least $k$ has a perfect $H$-subdivision …

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  • Rob Morris, Ramsey theory: searching for order in chaos

    Room 1501, Bldg. E6-1, KAIST

    In many different areas of mathematics (such as number theory, discrete geometry, and combinatorics), one is often presented with a large "unstructured" object, and asked to find a smaller "structured" object inside it. One of the earliest and most influential examples of this phenomenon was the theorem of Ramsey, proved in 1930, which states that …

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  • Rob Morris, An exponential improvement for diagonal Ramsey

    Room B332 IBS (기초과학연구원)

    The Ramsey number $R(k)$ is the minimum n such that every red-blue colouring of the edges of the complete graph on n vertices contains a monochromatic copy of $K_k$. It has been known since the work of Erdős and Szekeres in 1935, and Erdős in 1947, that $2^{k/2} < R(k) < 4^k$, but in the …

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  • Jozef Skokan, Separating the edges of a graph by a linear number of paths

    Room B332 IBS (기초과학연구원)

    Recently, Letzter proved that any graph of order n contains a collection P of $O(n \log^*n)$ paths with the following property: for all distinct edges e and f there exists a path in P which contains e but not f. We improve this upper bound to 19n, thus answering a question of Katona and confirming …

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  • Maria Chudnovsky, Induced subgraphs and tree decompositions

    Room 1501, Bldg. E6-1, KAIST

    Tree decompositions are a powerful tool in both structural graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. Tree decompositions …

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  • Oliver Janzer, Small subgraphs with large average degree

    Room B332 IBS (기초과학연구원)

    We study the fundamental problem of finding small dense subgraphs in a given graph. For a real number $s>2$, we prove that every graph on $n$ vertices with average degree at least $d$ contains a subgraph of average degree at least $s$ on at most $nd^{-\frac{s}{s-2}}(\log d)^{O_s(1)}$ vertices. This is optimal up to the polylogarithmic …

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  • Szymon Toruńczyk, Flip-width: Cops and Robber on dense graphs

    Zoom ID: 869 4632 6610 (ibsdimag)

    We define new graph parameters, called flip-width, that generalize treewidth, degeneracy, and generalized coloring numbers for sparse graphs, and clique-width and twin-width for dense graphs. The flip-width parameters are defined using variants of the Cops and Robber game, in which the robber has speed bounded by a fixed constant r∈N∪{∞}, and the cops perform flips …

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  • Suyun Jiang (江素云), How connectivity affects the extremal number of trees

    Room B332 IBS (기초과학연구원)

    The Erdős-Sós conjecture states that the maximum number of edges in an $n$-vertex graph without a given $k$-vertex tree is at most $\frac {n(k-2)}{2}$. Despite significant interest, the conjecture remains unsolved. Recently, Caro, Patkós, and Tuza considered this problem for host graphs that are connected. Settling a problem posed by them, for a $k$-vertex tree …

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