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June 2019

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Jinyoung Park (박진영), The number of maximal independent sets in the Hamming cube

Speaker

Jinyoung Park (박진영)
Department of Mathematics, Rutgers University, USA
https://sites.google.com/view/jinyoungpark
June 3 Monday @ 4:30 PM - 5:30 PM
Room B232, IBS (기초과학연구원)

Let $Q_n$ be the $n$-dimensional Hamming cube (hypercube) and $N=2^n$. We prove that the number of maximal independent sets in $Q_n$ is asymptotically $2n2^{N/4}$, as was conjectured by Ilinca and Kahn in connection with a question of Duffus, Frankl and Rödl. The value is a natural lower bound derived from a connection between maximal independent sets and induced matchings. The proof of the upper bound draws on various tools, among them "stability" results for maximal independent set counts and old…

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Suil O (오수일), An odd [1,b]-factor in regular graphs from eigenvalues

Speaker

Suil O (오수일)
Department of Applied Mathematics and Statistics, SUNY-Korea
https://you.stonybrook.edu/suilo/
June 19 Wednesday @ 4:30 PM - 5:30 PM
Room B232, IBS (기초과학연구원)

An odd $$-factor of a graph is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $1 \le d_H(v) \le b$, and $d_H(v)$ is odd. For positive integers $r \ge 3$ and $b \le r$, Lu, Wu, and Yang gave an upper bound for the third largest eigenvalue in an $r$-regular graph with even number of vertices to guarantee the existence of an odd -factor. In this talk, we improve their bound.

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Patrice Ossona de Mendez, A model theoretical approach to sparsity

June 25 Tuesday @ 4:30 PM - 5:30 PM
Room B232, IBS (기초과학연구원)

We discuss how the model theoretic notion of first-order transduction allows to define a notion of structural sparsity, and give some example of applications, like existence of low shrub-depth decompositions for tranductions of bounded expansion classes, characterization of transductions of classes with bounded pathwidth, decompositions of graphs with bounded rank-width into cographs.

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기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
Discrete Mathematics Group (DIMAG)
Center for Mathematical and Computational Sciences
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr
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