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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181214T110000
DTEND;TZID=America/New_York:20181214T120000
DTSTAMP:20190218T105411
CREATED:20180621T193833Z
LAST-MODIFIED:20181204T175526Z
UID:7926-1544785200-1544788800@idss.mit.edu
SUMMARY:Large girth approximate Steiner triple systems
DESCRIPTION: Abstract: In 1973 Erdos asked whether there are n-vertex partial Steiner triple systems with arbitrary high girth and quadratically many triples. (Here girth is defined as the smallest integer g \ge 4 for which some g-element vertex-set contains at least g-2 triples.) \nWe answer this question\, by showing existence of approximate Steiner triple systems with arbitrary high girth. More concretely\, for any fixed \ell \ge 4 we show that a natural constrained random process typically produces a partial Steiner triple system with (1/6-o(1))n^2 triples and girth larger than \ell. The process iteratively adds random triples subject to the constraint that the girth remains larger than \ell. Our result is best possible up to the o(1)-term\, which is a negative power of n. \nJoint work with Tom Bohman. \n
URL:https://idss.mit.edu/calendar/stochastics-and-statistics-seminar-22/
CATEGORIES:Stochastics and Statistics Seminar Series
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