  The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so
that our proof of Theorem A and Proposition B has an important gap. We were
unable to fix it yet. Any help is most welcome. We prove that the restriction
of surface minority to fiber surfaces of divides is a well-quasi-order. Here
surface minority is the partial order on isotopy classes of surfaces embedded
in the 3-space associated with incompressible subsurfaces. The proof relies on
a refinement of the Robertson-Seymour Theorem that involves colored graphs
embedded into the plane. Our result implies that every property of fiber
surfaces of divides that is preserved by surface minority is characterized by a
finite number of prohibited minors. For the signature to be equal to the first
Betti number is such a property. We explicitly determine the corresponding
prohibited minors. As an application we establish a correspondance between
divide links of maximal signature and Dynkin diagrams.
