The notion of tightness of a PL-embedding of a triangulated manifold is closely related to its property of being a Hamiltonian subcomplex of some convex polytope. Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplex-wise linear embedding of the triangulation into Euclidean space is "as convex as possible". It can thus be understood as a generalization of the concept of convexity.
In even dimensions, there exist purely combinatorial conditions which imply the tightness of a triangulation. In this work, other sufficient and purely combinatorial conditions which can be applied to the odd-dimensional case as well are presented.
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