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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
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DTSTART:20180101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191001T163000
DTEND;TZID=Asia/Seoul:20191001T173000
DTSTAMP:20260422T230751
CREATED:20190916T044737Z
LAST-MODIFIED:20240705T204218Z
UID:1387-1569947400-1569951000@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, Extremal problems for Berge hypergraphs
DESCRIPTION:Given a graph $G$\, there are several natural hypergraph families one can define. Among the least restrictive is the family $BG$ of so-called Berge copies of the graph $G$. In this talk\, we discuss Turán problems for families $BG$ in $r$-uniform hypergraphs for various graphs $G$. In particular\, we are interested in general results in two settings: the case when $r$ is large and $G$ is any graph where this Turán number is shown to be eventually subquadratic\, as well as the case when $G$ is a tree where several exact results can be obtained. The results in the first part are joint with Grósz and Methuku\, and the second part with Győri\, Salia and Zamora.
URL:https://dimag.ibs.re.kr/event/2019-10-01/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191010T163000
DTEND;TZID=Asia/Seoul:20191010T173000
DTSTAMP:20260422T230751
CREATED:20190710T015315Z
LAST-MODIFIED:20240707T090044Z
UID:1081-1570725000-1570728600@dimag.ibs.re.kr
SUMMARY:Alexandr V. Kostochka\, Reconstructing graphs from smaller subgraphs
DESCRIPTION:A graph or graph property is $\ell$-reconstructible if it is determined by the multiset of all subgraphs obtained by deleting $\ell$ vertices. Apart from the famous Graph Reconstruction Conjecture\, Kelly conjectured in 1957 that for each $\ell\in\mathbb N$\, there is an integer $n=n(\ell)$ such that every graph with at least $n$ vertices is $\ell$-reconstructible. \nWe show that for each $n\ge7$ and every $n$-vertex graph $G$\, the degree list and connectedness of $G$ are $3$-reconstructible\, and the threshold $n\geq 7$ is sharp for both properties.‌ We also show that all $3$-regular graphs are $2$-reconstructible.
URL:https://dimag.ibs.re.kr/event/2019-10-10/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191015T163000
DTEND;TZID=Asia/Seoul:20191015T173000
DTSTAMP:20260422T230751
CREATED:20190920T222934Z
LAST-MODIFIED:20240707T090036Z
UID:1409-1571157000-1571160600@dimag.ibs.re.kr
SUMMARY:Zi-Xia Song (宋梓霞)\, Ramsey numbers of  cycles under Gallai colorings
DESCRIPTION:For a graph $H$ and an integer $k\ge1$\, the $k$-color Ramsey number $R_k(H)$ is the least integer $N$ such that every $k$-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of $H$. Let $C_m$ denote the cycle on $m\ge4 $ vertices. For odd cycles\, Bondy and Erd\H{o}s in 1973 conjectured that for all $k\ge1$ and $n\ge2$\, $R_k(C_{2n+1})=n\cdot 2^k+1$. Recently\, this conjecture has been verified to be true for all fixed $k$ and all $n$ sufficiently large by Jenssen and Skokan; and false for all fixed $n$ and all $k$ sufficiently large by Day and Johnson. Even cycles behave rather differently in this context. Little is known about the behavior of $R_k(C_{2n})$ in general. In this talk we will present our recent results on Ramsey numbers of cycles under Gallai colorings\, where a Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles. We prove that the aforementioned conjecture holds for all $k$ and all $n$ under Gallai colorings. We also completely determine the Ramsey number of even cycles under Gallai colorings. \nJoint work with Dylan Bruce\, Christian Bosse\, Yaojun Chen and Fangfang Zhang.
URL:https://dimag.ibs.re.kr/event/2019-10-15/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191022T163000
DTEND;TZID=Asia/Seoul:20191022T173000
DTSTAMP:20260422T230751
CREATED:20190920T222518Z
LAST-MODIFIED:20240707T090027Z
UID:1407-1571761800-1571765400@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, On some properties of graph norms
DESCRIPTION: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. \nWe obtain some results that contribute to the theory of (weakly) norming graphs. Firstly\, we show that ‘twisted’ blow-ups of cycles\, which include $K_{5\,5}\setminus C_{10}$ and $C_6\square K_2$\, are not weakly norming. This answers two questions of Hatami\, who asked whether the two graphs are weakly norming. Secondly\, we prove that $\|.\|_{r(H)}$ is not uniformly convex nor uniformly smooth\, provided that $H$ is weakly norming. This answers another question of Hatami\, who estimated the modulus of convexity and smoothness of $\|.\|_{H}$. We also prove that every graph $H$ without isolated vertices is (weakly) norming if and only if each component is an isomorphic copy of a (weakly) norming graph. This strong factorisation result allows us to assume connectivity of $H$ when studying graph norms. Based on joint work with Frederik Garbe\, Jan Hladký\, and Bjarne Schülke.
URL:https://dimag.ibs.re.kr/event/2019-10-22/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191029T163000
DTEND;TZID=Asia/Seoul:20191029T173000
DTSTAMP:20260422T230751
CREATED:20191027T110551Z
LAST-MODIFIED:20240707T090010Z
UID:1632-1572366600-1572370200@dimag.ibs.re.kr
SUMMARY:Pascal Gollin\, A Cantor-Bernstein-type theorem for spanning trees in infinite graphs
DESCRIPTION:Given a cardinal $\lambda$\, a $\lambda$-packing of a graph $G$ is a family of $\lambda$ many edge-disjoint spanning trees of $G$\, and a $\lambda$-covering of $G$ is a family of spanning trees covering $E(G)$. \nWe show that if a graph admits a $\lambda$-packing and a $\lambda$-covering  then the graph also admits a decomposition into $\lambda$ many spanning trees. In this talk\, we concentrate on the case of $\lambda$ being an infinite cardinal. Moreover\, we will provide a new and simple proof for a theorem of Laviolette characterising the existence of a $\lambda$-packing\, as well as for a theorem of Erdős and Hajnal characterising the existence of a $\lambda$-covering.  \nJoint work with Joshua Erde\, Attila Joó\, Paul Knappe and Max Pitz.
URL:https://dimag.ibs.re.kr/event/2019-10-29/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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