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DTSTART:20250101T000000
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DTSTART;TZID=Asia/Seoul:20260915T163000
DTEND;TZID=Asia/Seoul:20260915T173000
DTSTAMP:20260821T131519Z
CREATED:20260821T131407Z
LAST-MODIFIED:20260821T131519Z
UID:13138-1789489800-1789493400@dimag.ibs.re.kr
SUMMARY:Gabriëlle Zwaneveld\, On Seymour-tight orientations
DESCRIPTION:I discuss ‘almost counterexamples’ to Seymour’s second neighbourhood conjecture. In what we call Seymour-tight orientations\, the size of the first neighbourhood of each vertex equals the size of its second neighbourhood. We give several examples and constructions. Specifically\, we prove that the class of Seymour-tight orientations is closed under taking (generalized) lexicographic products. Moreover\, the lexicographic product of a putative counterexample to Seymour’s second neighbourhood conjecture and a Seymour-tight orientation is again a counterexample. \nUsing lexicographic products\, we show that if the conjecture is false\, then there exist counterexamples that are close to regular tournaments\, and moreover that any digraph occurs as an induced subgraph of a counterexample. We then use this same machinery to construct special putative counterexamples to Sullivan’s conjecture. \nThe inherent symmetry of these orientations give access to an algebraic perspective. Seymour-tight orientations that are also Cayley digraphs correspond to special pairs of critical sets in groups\, which connects potentially to additive combinatorics. We use Kemperman’s theorem to characterize those Seymour-tight orientations that are the Cayley digraph of an abelian group.
URL:https://dimag.ibs.re.kr/event/2026-09-15/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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