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Hypergraph Saturation Irregularities

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  • UserNatalie Behague (QMUL)
  • ClockThursday 22 February 2018, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

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 creates 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 interesting counterpoint to the Turan number; the saturation number is in many ways 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 conjecture by finding a finite family of graphs, whose saturation number divided by n does not tend to a limit. We will prove a similar result for hypergraphs and discuss some variants.

This talk is part of the Combinatorics Seminar series.

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