Discrete Math Seminar

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  • Dabeen Lee (이다빈), Mixing sets, submodularity, and chance-constrained optimization

    Room B232 IBS (기초과학연구원)

    A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack constraint). In this talk, we first explain basic mixing sets by establishing a strong and previously unrecognized connection to submodularity. In particular, we …

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  • Kevin Hendrey, Extremal functions for sparse minors

    Room B232 IBS (기초과학연구원)

    The extremal function $c(H)$ of a graph $H$ is the supremum of densities of graphs not containing $H$ as a minor, where the density of a graph is the ratio of the number of edges to the number of vertices. Myers and Thomason (2005), Norin, Reed, Thomason and Wood (2020), and Thomason and Wales (2019) …

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  • Eunjin Oh (오은진), Feedback Vertex Set on Geometric Intersection Graphs

    Room B232 IBS (기초과학연구원)

    I am going to present an algorithm for computing a feedback vertex set of a unit disk graph of size k, if it exists, which runs in time $2^{O(\sqrt{k})}(n + m)$, where $n$ and $m$ denote the numbers of vertices and edges, respectively. This improves the $2^{O(\sqrt{k}\log k)}(n + m)$-time algorithm for this problem on unit disk …

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  • Joonkyung Lee (이준경), Majority dynamics on sparse random graphs

    Room B232 IBS (기초과학연구원)

    Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini, Chan, O'Donnell, Tamuz and Tan conjectured that, in the Erdős-Rényi random graph $G(n,p)$, the random initial $\pm 1$-assignment converges to a $99\%$-agreement with high …

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  • Donggyu Kim (김동규), 𝝘-graphic delta-matroids and their applications

    Room B232 IBS (기초과학연구원)

    Bouchet (1987) defined delta-matroids by relaxing the base exchange axiom of matroids. Oum (2009) introduced a graphic delta-matroid from a pair of a graph and its vertex subset. We define a $\Gamma$-graphic delta-matroid for an abelian group $\Gamma$, which generalizes a graphic delta-matroid. For an abelian group $\Gamma$, a $\Gamma$-labelled graph is a graph whose …

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  • Ben Lund, Maximal 3-wise intersecting families

    Room B232 IBS (기초과학연구원)

    A family $\mathcal F$ of subsets of {1,2,…,n} is called maximal k-wise intersecting if every collection of at most k members from $\mathcal F$ has a common element, and moreover, no set can be added to $\mathcal F$ while preserving this property. In 1974, Erdős and Kleitman asked for the smallest possible size of a …

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  • Jaehoon Kim (김재훈), 2-complexes with unique embeddings in 3-space

    Room B232 IBS (기초과학연구원)

    A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected 2-complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere, if it admits one at all. This can be thought of …

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  • Casey Tompkins, Ramsey numbers of Boolean lattices

    Room B232 IBS (기초과학연구원)

    The poset Ramsey number $R(Q_{m},Q_{n})$ is the smallest integer $N$ such that any blue-red coloring of the elements of the Boolean lattice $Q_{N}$ has a blue induced copy of $Q_{m}$ or a red induced copy of $Q_{n}$. Axenovich and Walzer showed that $n+2\le R(Q_{2},Q_{n})\le2n+2$. Recently, Lu and Thompson improved the upper bound to $\frac{5}{3}n+2$. In …

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  • Seonghyuk Im (임성혁), Large clique subdivisions in graphs without small dense subgraphs

    Room B232 IBS (기초과학연구원)

    What is the largest number $f(d)$ where every graph with average degree at least $d$ contains a subdivision of $K_{f(d)}$? Mader asked this question in 1967 and $f(d) = \Theta(\sqrt{d})$ was proved by Bollobás and Thomason and independently by Komlós and Szemerédi. This is best possible by considering a disjoint union of $K_{d,d}$. However, this …

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  • Eun-Kyung Cho (조은경), Independent domination of graphs with bounded maximum degree

    Room B232 IBS (기초과학연구원)

    The independent domination number of a graph $G$, denoted $i(G)$, is the minimum size of an independent dominating set of $G$. In this talk, we prove a series of results regarding independent domination of graphs with bounded maximum degree. Let $G$ be a graph with maximum degree at most $k$ where $k \ge 1$. We prove that …

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