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.
Hypergraph Saturation Irregularities
Natalie Behague (QMUL)
Fri, 01/12/2017 - 16:00
W316, Queen's Building