Kalai orientations on matroid polytopes

2005/04/15 by Raul Cordovil, Cordovil, Raul
Computer Science · Mathematics · #05B35 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #math.CO #msc:05B35

paper · pdf · doi:10.48550/arxiv.math/0504326

6 pages

arxiv created 2005/04/15 · openalex publication_date 2005/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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