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The 2nd Workshop on Developments in Combinatorics

Zoom ID: 346 934 4087 (202209)

Official website (with the abstract) https://www.ibs.re.kr/ecopro/online-workshop-developments-in-combinatorics/ Invited Speakers Nov. 28 Monday Jie Han, Beijing Institute of Technology 15:30 Seoul, 14:30 Beijing, 06:30 UK, 07:30 EU Joonkyung Lee (이준경), Hanyang University 16:10 Seoul, 15:10 Beijing, 07:10 UK, 08:10 EU Lior Gishboliner, ETH Zürich 16:50 Seoul, 15:50 Beijing, 07:50 UK, 08:50 EU Alex Scott, University of Oxford …

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Cosmin Pohoata, Convex polytopes from fewer points

Zoom ID: 224 221 2686 (ibsecopro)

Finding the smallest integer $N=ES_d(n)$ such that in every configuration of $N$ points in $\mathbb{R}^d$ in general position, there exist $n$ points in convex position is one of the most classical problems in extremal combinatorics, known as the Erdős-Szekeres problem. In 1935, Erdős and Szekeres famously conjectured that $ES_2(n)=2^{n−2}+1$ holds, which was nearly settled by …

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Giannos Stamoulis, Model-Checking for First-Order Logic with Disjoint Paths Predicates in Proper Minor-Closed Graph Classes

Room B332 IBS (기초과학연구원)

The disjoint paths logic, FOL+DP,  is an extension of First Order Logic (FOL) with the extra atomic predicate $\mathsf{dp}_k(x_1,y_1,\ldots,x_k,y_k),$ expressing the existence of internally vertex-disjoint paths between $x_i$ and $y_i,$ for $i\in \{1,\ldots, k\}$. This logic can express a wide variety of problems that escape the expressibility potential of FOL. We prove that for every …

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Maya Sankar, Homotopy and the Homomorphism Threshold of Odd Cycles

Zoom ID: 224 221 2686 (ibsecopro)

Fix $r \ge 2$ and consider a family F of $C_{2r+1}$-free graphs, each having minimum degree linear in its number of vertices. Such a family is known to have bounded chromatic number; equivalently, each graph in F is homomorphic to a complete graph of bounded size. We disprove the analogous statement for homomorphic images that …

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Stijn Cambie, The 69-conjecture and more surprises on the number of independent sets

Room B332 IBS (기초과학연구원)

Various types of independent sets have been studied for decades. As an example, the minimum number of maximal independent sets in a connected graph of given order is easy to determine (hint; the answer is written in the stars). When considering this question for twin-free graphs, it becomes less trivial and one discovers some surprising …

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Youngho Yoo (유영호), Approximating TSP walks in subcubic graphs

Room B332 IBS (기초과학연구원)

The Graphic Travelling Salesman Problem is the problem of finding a spanning closed walk (a TSP walk) of minimum length in a given connected graph. The special case of the Graphic TSP on subcubic graphs has been studied extensively due to their worst-case behaviour in the famous $\frac{4}{3}$-integrality-gap conjecture on the "subtour elimination" linear programming …

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Mamadou Moustapha Kanté, MSOL-Definable decompositions

Room B332 IBS (기초과학연구원)

I will first introduce the notion of recognisability of languages of terms and then its extensions to sets of relational structures. In a second step, I will discuss relations with decompositions of graphs/matroids and why their MSOL-definability is related to understanding recognisable sets. I will finally explain  how to define in MSOL branch-decompositions for finitely …

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Noleen Köhler, Twin-Width VIII: Delineation and Win-Wins

Room B332 IBS (기초과학연구원)

We introduce the notion of delineation. A graph class $\mathcal C$ is said delineated by twin-width (or simply, delineated) if for every hereditary closure $\mathcal D$ of a subclass of $\mathcal C$, it holds that $\mathcal D$ has bounded twin-width if and only if $\mathcal D$ is monadically dependent. An effective strengthening of delineation for …

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Pedro Montealegre, A Meta-Theorem for Distributed Certification

Zoom ID: 869 4632 6610 (ibsdimag)

Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a given boolean predicate. A certificate is assigned to each process in the system by a non-trustable oracle, and the processes are in charge of verifying these certificates, so that two …

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Jan Hladký, Invitation to graphons

Zoom ID: 224 221 2686 (ibsecopro)

The first course in graph theory usually covers concepts such as matchings, independent sets, colourings, and forbidden subgraphs. Around 2004, Borgs, Chayes, Lovász, Sós, Szegedy, and Vestergombi introduced a very fruitful limit perspective on graphs. The central objects of this theory, so-called graphons, are suitable measurable counterparts to graphs. In the talk, I will outline …

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IBS 이산수학그룹 Discrete Mathematics Group
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