%0 Unpublished work %T Laminations of a graph on a pair of pants %+ Unité de Mathématiques Pures et Appliquées (UMPA-ENSL) %A Ramassamy, Sanjay %8 2018-04-05 %D 2018 %Z Mathematics [math]/Combinatorics [math.CO] %Z Mathematics [math]/Geometric Topology [math.GT]Preprints, Working Papers, ... %X A 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. %G English %2 https://ens-lyon.hal.science/ensl-01759975v1/document %2 https://ens-lyon.hal.science/ensl-01759975v1/file/PantsLaminations.pdf %L ensl-01759975 %U https://ens-lyon.hal.science/ensl-01759975