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 simplified variant 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.

中文翻译：

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图在一条裤子上的叠片

嵌入在表面上的图的分层是在图上绘制的成对不相交的不可收缩的简单闭合曲线的集合。在表面是具有三个刺孔（又称为一条裤子）的球体的情况下，我们首先将嵌入该表面的图形的层压空间标识为格子多边形，然后将多边形表征为一条裤子上的一些图形。这表征了矢量束拉普拉斯算子的频谱图的简化变体的图像，用于一条裤子上的扁平连接。该证明使用类似于平面地图剥离的图探索技术。