A super-balanced hypergraph has a nest point
Andries E. Brouwer, Antoon W. J. Kolen · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1980
A super-balanced hypergraph is a hyperqraph such that in any cycle of length at least three there is an edge containing at least three vertices of the cycle.A nest point is a vertex such that the edges containing it are totally ordered by inclusion.It is proved that a super-balanced hypergraph contains at least two nest points.