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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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TZID:Asia/Seoul
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DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220310T163000
DTEND;TZID=Asia/Seoul:20220310T173000
DTSTAMP:20260419T130104
CREATED:20220310T073000Z
LAST-MODIFIED:20240705T174146Z
UID:5176-1646929800-1646933400@dimag.ibs.re.kr
SUMMARY:Fedor Fomin\, Long cycles in graphs: Extremal Combinatorics meets Parameterized Algorithms
DESCRIPTION:We examine algorithmic extensions of two classic results of extremal combinatorics. First\, the theorem of Dirac from 1952 asserts that a 2-connected graph G with the minimum vertex degree d>1\, is either Hamiltonian or contains a cycle of length at least 2d. Second\, the theorem of Erdős-Gallai from 1959\, states that a 2-connected graph G with the average vertex degree D>1\, contains a cycle of length at least D. \nWe discuss the recent progress in parameterized complexity of computing long cycles “above” the guarantees established by these classical theorems: cycles of lengths at least 2d+k and D+k. \nThe talk is based on the joint works with Petr Golovach\, Danil Sagunov\, and Kirill Simonov.
URL:https://dimag.ibs.re.kr/event/2022-03-10/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220330T163000
DTEND;TZID=Asia/Seoul:20220330T173000
DTSTAMP:20260419T130104
CREATED:20220330T073000Z
LAST-MODIFIED:20240707T080136Z
UID:5270-1648657800-1648661400@dimag.ibs.re.kr
SUMMARY:Jean-Florent Raymond\, Long induced paths in minor-closed graph classes and beyond
DESCRIPTION:In 1982 Galvin\, Rival\, and Sands proved that in $K_{t\,t}$-subgraph free graphs (t being fixed)\, the existence of a path of order n guarantees the existence of an induced path of order f(n)\, for some (slowly) increasing function f. The problem of obtaining good lower-bounds for f for specific graph classes was investigated decades later and logarithmic bounds have been obtained for planar graphs (more generally for graphs of bounded genus) and for interval graphs. \nIn this talk I will show that every graph of pathwidth less than k that has a path of order n also has an induced path of order $Ω(n^{1/k})$. I will then explain how this result can be used to prove the two following generalizations: \n\nevery graph of treewidth less than k that has a path of order n contains an induced path of order $Ω((\log n)^{1/k})$;\nfor every non-trivial graph class that is closed under topological minors there is a constant d∈(0\,1) such that every graph from this class that has a path of order n contains an induced path of order $Ω((\log n)^d)$.\n\nJoint work with Claire Hilaire.
URL:https://dimag.ibs.re.kr/event/2022-03-30/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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