2010/11/28 by Andrey O. Matveev, Matveev, Andrey O. · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1011.6082
openalex publication_date 2010/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let the sign components of the maximal covectors of a simple oriented matroid M be represented by the real numbers -1 and 1. Consider the vertex set V(R) of a symmetric cycle R of adjacent topes in the tope graph of M as a subposet of the tope poset of M. If B is the bottom element of the tope poset then B is equal to the unweighted sum of the members of the set min V(R) of minimal elements of the subposet V(R); if B is the positive tope then the set min V(R) is a critical tope committee for the acyclic oriented matroid M.