Part of the Lecture Notes in Computer Science book series (LNCS, volume 1731)
Geometric Realization of Simplicial Complexes
We show that an abstract simplicial complex Δ may be realized on a grid of IRd-1, where d = dim P(Δ) is the order dimension (Dushnik-Miller dimension) of the face poset of Δ.
KeywordsPlanar Graph Linear Order Simplicial Complex Maximal Element Total Order
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