  An $n$-Venn diagram is a certain collection of $n$ simple closed curves in
the plane. They can be regarded as graphs where the points of intersection are
vertices and the curve segments between points of intersection are edges. Every
$n$-Venn diagram has the property that a curve touches any given face at most
once between the points of intersection incident to that face. We prove that
any connected collection of $n$ simple closed curves satisfying that property
are 4-connected, if $n \ge 3$, so long as the curves intersect transversally
and at most two curves intersect at any point. Hence by a theorem of Tutte,
such collections, including simple Venn diagrams, are Hamiltonian.
