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SUMMARY:Hypergraph Saturation Irregularities - Natalie Behague (QMUL) 
DTSTART:20180222T143000Z
DTEND:20180222T153000Z
UID:TALK100435@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:We say that a graph G is saturated with respect to some graph 
 F if G doesn't contain any copies of F but adding any new edge to G create
 s some copy of F. The saturation number sat(F\,n) is the minimum number of
  edges an F-saturated graph on n vertices can have. This forms an interest
 ing counterpoint to the Turan number\; the saturation number is in many wa
 ys less well-behaved. For example\, Tuza conjectured that sat(F\,n)/n must
  tend to a limit as n tends to infinity and this is still open. However\, 
 Pikhurko disproved a strengthening of Tuza's\nconjecture by finding a fini
 te family of graphs\, whose saturation number divided by n does not tend t
 o a limit. We will prove a similar result for hypergraphs\nand discuss som
 e variants.\n
LOCATION:MR12
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