An intersecting family is a family 
of sets such that 
for every 
. A 
-uniform intersecting family has 
for every 
. A hitting set, also called
a cover, meets every member of 
. The minimum size of such a hitting
set is the covering number 
.
Extremal sizes of intersecting families can change when the covering number is prescribed. The Frankl-Ota-Tokushige conjecture concerns the largest number of minimum hitting sets in a uniform intersecting family (Patkós 2026).
