https://ens-lyon.hal.science/ensl-01759975v1Ramassamy, SanjaySanjayRamassamyUMPA-ENSL - Unité de Mathématiques Pures et Appliquées - ENS de Lyon - École normale supérieure de Lyon - CNRS - Centre National de la Recherche ScientifiqueLaminations of a graph on a pair of pantsHAL CCSD2018[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Ramassamy, Sanjay2018-04-05 19:41:272023-05-11 11:56:092018-04-06 09:12:22enPreprints, Working Papers, ...https://ens-lyon.hal.science/ensl-01759975v2application/pdf1A lamination of a graph embedded on a surface is a collection of pair-wise 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.