BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20200101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210302T163000
DTEND;TZID=Asia/Seoul:20210302T173000
DTSTAMP:20260419T082822
CREATED:20210217T044249Z
LAST-MODIFIED:20240707T081721Z
UID:3639-1614702600-1614706200@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, A unified half-integral 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. Such a duality does not hold if we restrict to odd cycles.  However\, in 1999\, Reed proved an analogue for odd cycles by relaxing packing to half-integral packing. We prove a far-reaching generalisation of the theorem of Reed; if the edges of a graph are labelled by finitely many abelian groups\, then there is a duality between the maximum size of a half-integral packing of cycles whose values avoid a fixed finite set for each abelian group and the minimum size of a vertex set hitting all such cycles. \nA multitude of natural properties of cycles can be encoded in this setting\, for example cycles of length at least $\ell$\, cycles of length $p$ modulo $q$\, cycles intersecting a prescribed set of vertices at least $t$ times\, and cycles contained in given $\mathbb{Z}_2$-homology classes in a graph embedded on a fixed surface. Our main result allows us to prove a duality theorem for cycles satisfying a fixed set of finitely many such properties. \nThis is joint work with J. Pascal Gollin\, Ken-ichi Kawarabayashi\, O-joung Kwon\, and Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2021-03-02/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR