Let 
be a graph. A hypergraph 
is a Berge 
if there is a bijection 
such that
 |
for every graph edge 
of 
. The vertices of each graph
edge are therefore contained in its corresponding hyperedge,
but a hyperedge may contain additional vertices.
A hypergraph is Berge 
-free if it contains no Berge 
as a subhypergraph.
A Berge cycle of length 
is an alternating sequence of
distinct vertices and distinct hyperedges
 |
with 
,
where subscripts are read cyclically. Thus it is a Berge 
. Dong et al. (2026) give spectral
radius bounds for Berge 
-free linear hypergraphs.
-Free
Linear 
-Graphs."
Electron. J. Combin. 33, P3.82, 2026.