  There exists a (relatively minimal) genus g Lefschetz fibration with only one
singular fiber over a closed (Riemann) surface of genus h iff g>2 and h>1. The
singular fiber can be chosen to be reducible or irreducible. Other results are
that every Dehn twist on a closed surface of genus at least three is a product
of two commutators and no Dehn twist on any closed surface is equal to a single
commutator.

Geometric Topology;Symplectic Geometry