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PRODID:-//Discrete Mathematics Group - ECPv6.16.2//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
TZNAME:KST
DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220307T163000
DTEND;TZID=Asia/Seoul:20220307T173000
DTSTAMP:20260525T183510
CREATED:20220307T073000Z
LAST-MODIFIED:20240705T174154Z
UID:5315-1646670600-1646674200@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups (revisited)
DESCRIPTION:This talk follows on from the recent talk of Pascal Gollin in this seminar series\, but will aim to be accessible for newcomers. \nErdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. By relaxing `packing’ to `half-integral packing’\, Reed obtained an analogous result for odd cycles\, and gave a structural characterisation of when the (integral) packing version fails. \nWe prove some far-reaching generalisations of these theorems. First\, we show that if the edges of a graph are labelled by finitely many abelian groups\, then the cycles whose values avoid a fixed finite set for each abelian group satisfy the half-integral Erdős-Pósa property. Similarly to Reed\, we give a structural characterisation for the failure of the integral Erdős-Pósa property in this setting. This allows us to deduce the full Erdős-Pósa property for many natural classes of cycles. \nWe will look at applications of these results to graphs embedded on surfaces\, and also discuss some possibilities and obstacles for extending these results. \nThis is joint work with Kevin Hendrey\, Ken-ichi Kawarabayashi\, O-joung Kwon\, Sang-il Oum\, and Youngho Yoo.
URL:https://dimag.ibs.re.kr/event/2022-03-07/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220314T163000
DTEND;TZID=Asia/Seoul:20220314T173000
DTSTAMP:20260525T183510
CREATED:20220314T073000Z
LAST-MODIFIED:20240705T174136Z
UID:5218-1647275400-1647279000@dimag.ibs.re.kr
SUMMARY:Tuan Anh Do\, Rank- and tree-width of supercritical random graphs
DESCRIPTION:It is known that the rank- and tree-width of the random graph $G(n\,p)$ undergo a phase transition at $p = 1/n$; whilst for subcritical $p$\, the rank- and tree-width are bounded above by a constant\, for supercritical $p$\, both parameters are linear in $n$. The known proofs of these results use as a black box an important theorem of Benjamini\, Kozma\, and Wormald on the expansion of supercritical random graphs. We give a new\, short\, and direct proof of these results\, leading to more explicit bounds on these parameters\, and also consider the rank- and tree-width of supercritical random graphs closer to the critical point\, showing that this phase transition is smooth. \nThis is joint work with Joshua Erde and Mihyun Kang.
URL:https://dimag.ibs.re.kr/event/2022-03-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220321T163000
DTEND;TZID=Asia/Seoul:20220321T173000
DTSTAMP:20260525T183510
CREATED:20220321T073000Z
LAST-MODIFIED:20240707T080150Z
UID:5277-1647880200-1647883800@dimag.ibs.re.kr
SUMMARY:Jaehoon Kim (김재훈)\, Ramsey numbers of cycles versus general graphs
DESCRIPTION:The Ramsey number $R(F\,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains a copy of $F$ or its complement contains $H$. Burr in 1981 proved a pleasingly general result that for any graph $H$\, provided $n$ is sufficiently large\, a natural lower bound construction gives the correct Ramsey number involving cycles: $R(C_n\,H)=(n-1)(\chi(H)-1)+\sigma(H)$\, where $\sigma(H)$ is the minimum possible size of a colour class in a $\chi(H)$-colouring of $H$. Allen\, Brightwell and Skokan conjectured that the same should be true already when $n\geq |H|\chi(H)$. \nWe improve this 40-year-old result of Burr by giving quantitative bounds of the form $n\geq C|H|\log^4\chi(H)$\, which is optimal up to the logarithmic factor. In particular\, this proves a strengthening of the Allen-Brightwell-Skokan conjecture for all graphs $H$ with large chromatic number. \nThis is joint work with John Haslegrave\, Joseph Hyde and Hong Liu
URL:https://dimag.ibs.re.kr/event/2022-03-21/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220328T163000
DTEND;TZID=Asia/Seoul:20220328T173000
DTSTAMP:20260525T183510
CREATED:20220314T051725Z
LAST-MODIFIED:20240707T080143Z
UID:5383-1648485000-1648488600@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Thresholds for incidence properties in finite vector spaces
DESCRIPTION:Suppose that $E$ is a subset of $\mathbb{F}_q^n$\, so that each point is contained in $E$ with probability $\theta$\, independently of all other points. Then\, what is the probability that there is an $m$-dimensional affine subspace that contains at least $\ell$ points of $E$? What is the probability that $E$ intersects all $m$-dimensional affine subspaces? We give Erdős-Renyi threshold functions for these properties\, in some cases sharp thresholds. Our results improve previous work of Chen and Greenhill. This is joint work with Jeong Han Kim\, Thang Pham\, and Semin Yoo.
URL:https://dimag.ibs.re.kr/event/2022-03-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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