1997/11/01 by Graham Brightwell, William T. Trotter · 1 citation
Computer Science · Engineering · Mathematics · #Graph Labeling and Dimension Problems #graph theory and CDMA systems #Advanced Graph Theory Research #Combinatorics #Dimension (graph theory) #Mathematics #Polytope #Planar #Partially ordered set #Order (exchange) #Regular polygon #Convex polytope #Planar graph #Discrete mathematics #Convex set #Geometry #Computer science #Graph #Convex optimization
paper · doi:10.1137/s0895480192238561
openalex publication_date 1997/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
This is a sequel to a previous paper entitled The Order Dimension of Convex Polytopes, by the same authors [SIAM J. Discrete Math., 6 (1993), pp. 230--245]. In that paper, we considered the poset \bf P\protect\boldmathM formed by taking the vertices, edges, and faces of a 3-connected planar map \bf M, ordered by inclusion, and showed that the order dimension of \bf P\protect\boldmathM is always equal to 4. In this paper, we show that if \bf M is any planar map, then the order dimension of \bf P\protect\boldmathM is still at most 4.