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Kalai orientations on matroid polytopes

Raul Cordovil
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Abstract

Let P a polytope and let G(P) be the graph of P. Following Gil Kalai, we say that an acyclic orientation O of G(P) is good if, for every non-empty face F of P, the induced graph G(F) has exactly one sink. Gil Kalai gave a simple way to tell a simple polytope from the good orientations of its graph. This article is a broader study of ``good orientations'' (of the graphs) on matroid polytopes.

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Raul Cordovil. 2005-04-15. Kalai orientations on matroid polytopes. https://arxiv.org/abs/math/0504326

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