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Sang-il Oum (엄상일), Obstructions for matroids of path-width at most k and graphs of linear rank-width at most k

Room B232 IBS (기초과학연구원)

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 $\mathbb F$, the list contains only finitely many $\mathbb F$-representable matroids, due to the well-quasi-ordering of $\mathbb F$-representable matroids of bounded …

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Kevin Hendrey, A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups (revisited)

Room B232 IBS (기초과학연구원)

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 …

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Fedor Fomin, Long cycles in graphs: Extremal Combinatorics meets Parameterized Algorithms

Zoom ID: 869 4632 6610 (ibsdimag)

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 …

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Tuan Anh Do, Rank- and tree-width of supercritical random graphs

Room B232 IBS (기초과학연구원)

It is known that the rank- and tree-width of the random graph $G(n,p)$ undergo a phase transition at $p = 1/n$; whilst for subcritical $p$, the rank- and tree-width are bounded above by a constant, for supercritical $p$, both parameters are linear in $n$. The known proofs of these results use as a black box an important theorem of …

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MATRIX-IBS Workshop: Structural Graph Theory Downunder II

MATRIX, Australia

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, …

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Jaehoon Kim (김재훈), Ramsey numbers of cycles versus general graphs

Room B232 IBS (기초과학연구원)

The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains a copy of $F$ or its complement contains $H$. Burr in 1981 proved a pleasingly general result that for any graph $H$, provided $n$ is sufficiently large, a natural lower bound construction gives the correct Ramsey number involving cycles: …

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Ben Lund, Thresholds for incidence properties in finite vector spaces

Room B232 IBS (기초과학연구원)

Suppose that $E$ is a subset of $\mathbb{F}_q^n$, so that each point is contained in $E$ with probability $\theta$, independently of all other points. Then, what is the probability that there is an $m$-dimensional affine subspace that contains at least $\ell$ points of $E$? What is the probability that $E$ intersects all $m$-dimensional affine subspaces? …

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Jean-Florent Raymond, Long induced paths in minor-closed graph classes and beyond

Zoom ID: 869 4632 6610 (ibsdimag)

In 1982 Galvin, Rival, and Sands proved that in $K_{t,t}$-subgraph free graphs (t being fixed), the existence of a path of order n guarantees the existence of an induced path of order f(n), for some (slowly) increasing function f. The problem of obtaining good lower-bounds for f for specific graph classes was investigated decades later …

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IBS ECOPRO Opening conference

Zoom ID: 878 0445 3986 (ibsecopro) [CLOSED]

To celebrate the opening of the IBS ECOPRO (Extremal Combinatorics and Probability) Group, we will organize a 3-day online conference from April 4 to April 6. Official Website: https://www.ibs.re.kr/ecopro/event/opening/ Invited Speakers Noga Alon Princeton University József Balogh University of Illinois at Urbana-Champaign Jeff Kahn Rutgers University Mihyun Kang Graz University of Technology Jeong Han Kim …

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IBS 이산수학그룹 Discrete Mathematics Group
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
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