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X-WR-CALDESC:Events for Discrete Mathematics Group
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DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220518T163000
DTEND;TZID=Asia/Seoul:20220518T173000
DTSTAMP:20260419T093710
CREATED:20220518T073000Z
LAST-MODIFIED:20240705T173008Z
UID:5506-1652891400-1652895000@dimag.ibs.re.kr
SUMMARY:Jan Kurkofka\, Canonical Graph Decompositions via Coverings
DESCRIPTION:We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph\, as determined by the relative position of these parts\, is described by a coarser model. This is a simpler graph determined entirely by the decomposition\, not imposed. \nThe model and decomposition are obtained as projections of the tangle-tree structure of a covering of the given graph that reflects its local structure at the intended level of locality while unfolding its global structure. \nOur theorem extends to locally finite quasi-transitive graphs and in particular to locally finite Cayley graphs. It thereby offers a canonical decomposition theorem for finitely generated groups into local parts\, whose relative structure is displayed by a graph. \nJoint work with Reinhard Diestel\, Raphael W. Jacobs and Paul Knappe.
URL:https://dimag.ibs.re.kr/event/2022-05-18/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220525T163000
DTEND;TZID=Asia/Seoul:20220525T173000
DTSTAMP:20260419T093710
CREATED:20220525T073000Z
LAST-MODIFIED:20240705T172235Z
UID:5509-1653496200-1653499800@dimag.ibs.re.kr
SUMMARY:Sebastian Siebertz\, Transducing paths in graph classes with unbounded shrubdepth
DESCRIPTION:Transductions are a general formalism for expressing transformations of graphs (and more generally\, of relational structures) in logic. We prove that a graph class C can be FO-transduced from a class of bounded-height trees (that is\, has bounded shrubdepth) if\, and only if\, from C one cannot FO-transduce the class of all paths. This establishes one of the three remaining open questions posed by Blumensath and Courcelle about the MSO-transduction quasi-order\, even in the stronger form that concerns FO-transductions instead of MSO-transductions. \nThe backbone of our proof is a graph-theoretic statement that says the following: If a graph G excludes a path\, the bipartite complement of a path\, and a half-graph as semi-induced subgraphs\, then the vertex set of G can be partitioned into a bounded number of parts so that every part induces a cograph of bounded height\, and every pair of parts semi-induce a bi-cograph of bounded height. This statement may be of independent interest; for instance\, it implies that the graphs in question form a class that is linearly chi-bounded. \nThis is joint work with Patrice Ossona de Mendez and Michał Pilipczuk.
URL:https://dimag.ibs.re.kr/event/2022-05-25/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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