  A lamination of a graph embedded on a surface is a collection of pairwise
disjoint non-contractible simple closed curves drawn on the graph. In the case
when the surface is a sphere with three punctures (a.k.a. a pair of pants), we
first identify the lamination space of a graph embedded on that surface as a
lattice polytope, then we characterize the polytopes that arise as the
lamination space of some graph on a pair of pants. This characterizes the image
of a purely topological version of the spectral map for the vector bundle
Laplacian for a flat connection on a pair of pants. The proof uses a graph
exploration technique akin to the peeling of planar maps.
