  Recently, Honda, Kazez and Matic described an adapted partial open book of a
compact contact 3-manifold with convex boundary by generalizing the work of
Giroux in the closed case. They also implicitly established a one-to-one
correspondence between isomorphism classes of partial open book decompositions
modulo positive stabilization and isomorphism classes of compact contact
3-manifolds with convex boundary. In this expository article we explicate the
relative version of Giroux correspondence.
