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The polytope of non-crossing graphs on a planar point set.

D. Orden, F. Santos

 

For any finite set A of n points in general position in R^2, we define a (3n-3)-dimensional simple polyhedron whose face poset is isomorphic to the poset of "non-crossing marked graphs" with vertex set A, where a marked graph is defined as a geometric graph together with a subset of its pointed vertices. The poset of non-crossing graphs on A appears as the complement of the star of a face in that polyhedron.

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