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PRODID:-//Discrete Mathematics Group - ECPv6.0.4//NONSGML v1.0//EN
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X-WR-CALNAME:Discrete Mathematics Group
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:20190101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220208T163000
DTEND;TZID=Asia/Seoul:20220208T173000
DTSTAMP:20221128T013103
CREATED:20220208T073000Z
LAST-MODIFIED:20220126T085511Z
UID:5159-1644337800-1644341400@dimag.ibs.re.kr
SUMMARY:Pascal Gollin\, A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
DESCRIPTION:Erdős 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. We therefore say that cycles satisfy the Erdős-Pósa property. However\, while odd cycles do not satisfy the Erdős-Pósa property\, Reed proved in 1999 an analogue by relaxing packing to half-integral packing\, where each vertex is allowed to be contained in at most two such cycles. Moreover\, he gave a structural characterisation for when the Erdős-Pósa property for odd cycles fails. \nWe prove a far-reaching generalisation of the theorem of Reed; 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\, and we similarly give a structural characterisation for the failure of the Erdős-Pósa property. \nA multitude of natural properties of cycles can be encoded in this setting. For example\, we show that the cycles of length $\ell$ modulo $m$ satisfy the half-integral Erdős-Pósa property\, and we characterise for which values of $\ell$ and $m$ these cycles satisfy the Erdős-Pósa property. \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/2022-02-08/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210518T163000
DTEND;TZID=Asia/Seoul:20210518T173000
DTSTAMP:20221128T013103
CREATED:20210420T015329Z
LAST-MODIFIED:20210510T090557Z
UID:3967-1621355400-1621359000@dimag.ibs.re.kr
SUMMARY:Pascal Gollin\, Enlarging vertex-flames in countable digraphs
DESCRIPTION:A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all ingoing edges of v. It was shown by Lovász that every finite rooted digraph admits a spanning subdigraph which is a vertex-flame and large\, where the latter means that it preserves the local connectivity to each vertex from the root. A structural generalisation of vertex-flames and largeness to infinite digraphs was given by Joó and the analogue of Lovász’ result for countable digraphs was shown. \nIn this talk\, I present a strengthening of this result stating that in every countable rooted digraph each vertex-flame can be extended to a large vertex-flame. \nJoint work with Joshua Erde and Attila Joó.
URL:https://dimag.ibs.re.kr/event/2021-05-18/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200407T163000
DTEND;TZID=Asia/Seoul:20200407T173000
DTSTAMP:20221128T013103
CREATED:20200403T043936Z
LAST-MODIFIED:20200629T005854Z
UID:2269-1586277000-1586280600@dimag.ibs.re.kr
SUMMARY:Pascal Gollin\, Disjoint dijoins for classes of dibonds in finite and infinite digraphs
DESCRIPTION:A dibond in a directed graph is a bond (i.e. a minimal non-empty cut) for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digraph the least size of an edge set meeting every dicut equals the maximum number of disjoint dibonds in that digraph. We call such sets dijoins. \nWoodall conjectured a dual statement. He asked whether the maximum number of disjoint dijoins in a digraph equals the minimum size of a dibond.\nWe study a modification of this question where we restrict our attention to certain classes of dibonds\, i.e. whether for a class $\mathfrak{B}$ of dibonds of a digraph the maximum number of disjoint edge sets meeting every dibond in $\mathfrak{B}$ equal the size a minimum dibond in $\mathfrak{B}$. \nIn particular\, we verify this questions for nested classes of dibonds\, for the class of dibonds of minimum size\, and for classes of infinite dibonds.
URL:https://dimag.ibs.re.kr/event/2020-04-07/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191029T163000
DTEND;TZID=Asia/Seoul:20191029T173000
DTSTAMP:20221128T013103
CREATED:20191027T110551Z
LAST-MODIFIED:20200629T010027Z
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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