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DTSTART:20190101T000000
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DTSTART;TZID=Asia/Seoul:20201119T163000
DTEND;TZID=Asia/Seoul:20201119T173000
DTSTAMP:20260423T043522
CREATED:20200927T025647Z
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UID:3062-1605803400-1605807000@dimag.ibs.re.kr
SUMMARY:Yijia Chen (陈翌佳)\, Graphs of bounded shrub-depth\, through a logic lens
DESCRIPTION:Shrub-depth is a graph invariant often considered as an extension\nof tree-depth to dense graphs. In this talk I will explain our recent\nproofs of two results about graphs of bounded shrub-depth. \n\nEvery graph property definable in monadic-second order logic\,\ne.g.\, 3-colorability\, can be evaluated by Boolean circuits of constant\ndepth and polynomial size\, whose depth only depends on the\nshrub-depth of input graphs.\nGraphs of bounded shrub-depth can be characterized by\na finite set of forbidden induced subgraphs [Ganian et al. 2015].\n\nCentral to the first result is the definability in first-order logic of\ntree-models for graphs of bounded shrub-depth. For the second\nresult\, we observe that shrub-depth can be easily generalized\nto infinite graphs\, and thus some classical tools\, i.e.\, Craig’s\nInterpolation and Łoś-Tarski Theorem\, in model theory are\napplicable to graphs of bounded shrub-depth. \nThis is joint work with Jörg Flum.
URL:https://dimag.ibs.re.kr/event/2020-11-19/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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