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DTSTART;TZID=Asia/Seoul:20210630T170000
DTEND;TZID=Asia/Seoul:20210630T180000
DTSTAMP:20260420T060617
CREATED:20210617T062135Z
LAST-MODIFIED:20240707T081259Z
UID:4277-1625072400-1625076000@dimag.ibs.re.kr
SUMMARY:Florian Gut and Attila Joó\, Large vertex-flames in uncountable digraphs
DESCRIPTION:The local connectivity  $ \kappa_D(r\,v) $ from $ r $ to $ v $ is defined to be the maximal number of internally disjoint $r\rightarrow v $ paths in $ D $. A spanning subdigraph $ L $ of $ D $ with $  \kappa_L(r\,v)=\kappa_D(r\,v) $ for every $ v\in V-r $ must have at least $ \sum_{v\in V-r}\kappa_D(r\,v) $ edges. It was shown by Lovász that\, maybe surprisingly\, this lower bound is sharp for every finite digraph. The optimality of an $ L $ can be captured by the following characterization: For every $ v\in V-r $ there is a system $ \mathcal{P}_v $ of internally disjoint $ r\rightarrow v $ paths in $ L $ covering all the ingoing edges of $ v $ in $ L $ such that one can choose from  each $ P\in \mathcal{P}_v $ either an edge or an internal vertex in such a way that the resulting set meets every $ r\rightarrow v $ path of $ D $. We prove that every digraph of size at most $ \aleph_1 $  admits such a spanning subdigraph $ L $. The question if this remains true for larger digraphs remains open.
URL:https://dimag.ibs.re.kr/event/2021-06-30/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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