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October 2019

:

Joonkyung Lee (이준경), On some properties of graph norms

Speaker

Joonkyung Lee (이준경)
Department of Mathematics, University of Hamburg, Germany
https://sites.google.com/site/joonkyungleemaths/
October 22 Tuesday @ 4:30 PM - 5:30 PM
Room B232, IBS (기초과학연구원)

For a graph $H$, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions $W$ in $L^p$, $p\geq e(H)$, denoted by $t_H(W)$. One may then define corresponding functionals $\|W\|_{H}:=|t_H(W)|^{1/e(H)}$ and $\|W\|_{r(H)}:=t_H(|W|)^{1/e(H)}$ and say that $H$ is (semi-)norming if $\|.\|_{H}$ is a (semi-)norm and that $H$ is weakly norming if $\|.\|_{r(H)}$ is a norm. We obtain some results that contribute to the theory of (weakly) norming graphs. Firstly, we show that 'twisted' blow-ups of cycles, which include…

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November 2019

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Tony Huynh, Stable sets in graphs with bounded odd cycle packing number

November 12 Tuesday @ 4:30 PM - 5:30 PM
Room B232, IBS (기초과학연구원)

It is a classic result that the maximum weight stable set problem is efficiently solvable for bipartite graphs.  The recent bimodular algorithm of Artmann, Weismantel and Zenklusen shows that it is also efficiently solvable for graphs without two disjoint odd cycles.  The complexity of the stable set problem for graphs without $k$ disjoint odd cycles is a long-standing open problem for all other values of $k$.  We prove that under the additional assumption that the input graph is embedded in a…

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:

Ruth Luo, Induced Turán problems for hypergraphs

Speaker

Ruth Luo
University of California, San Diego
https://faculty.math.illinois.edu/~ruthluo2/
November 19 Tuesday @ 4:30 PM - 5:30 PM
Room B232, IBS (기초과학연구원)

Let $F$ be a graph. We say that a hypergraph $\mathcal H$ is an induced Berge $F$ if there exists a bijective mapping $f$ from the edges of $F$ to the hyperedges of $\mathcal H$ such that for all $xy \in E(F)$, $f(xy) \cap V(F) = \{x,y\}$. In this talk, we show asymptotics for the maximum number of edges in $r$-uniform hypergraphs with no induced Berge $F$. In particular, this function is strongly related to the generalized Turán function $ex(n,K_r, F)$, i.e., the…

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December 2019

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Jakub Gajarský, First-order interpretations of bounded expansion classes

December 10 Tuesday @ 4:30 PM - 5:30 PM
Room B232, IBS (기초과학연구원)

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined as first-order interpretations of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes of bounded expansion via low…

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