  In this note we introduce the (homologically essential) arc complex of a
surface as a tool for studying properties of open book decompositions and
contact structures. After characterizing destabilizability in terms of the
essential translation distance of the monodromy of an open book we given an
application of this result to show that there are planer open books of the
standard contact structure on the 3-sphere with 5 (or any number larger than 5)
boundary components that do not destabilize. We also show that any planar open
book with 4 or fewer boundary components does destabilize.
