  We employ a certain labeled finite graph, called a chart, in a closed
oriented surface for describing the monodromy of a(n achiral) Lefschetz
fibration over the surface. Applying charts and their moves with respect to
Wajnryb's presentation of mapping class groups, we first generalize a signature
formula for Lefschetz fibrations over the 2-sphere obtained by Endo and Nagami
to that for Lefschetz fibrations over arbitrary closed oriented surface. We
then show two theorems on stabilization of Lefschetz fibrations under fiber
summing with copies of a typical Lefschetz fibration as generalizations of a
theorem of Auroux.
