The Order Dimension of Planar Maps
Authors:
- Graham R. BrightwellGBGraham R. Brightwell
- William T. TrotterWTWilliam T. Trotter
- 1 November 1997
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Discrete Mathematics
- Vol. 10 (4) , 515-528
Abstract
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\boldmath$_M\!\!\!$} 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\boldmath$_M\!\!\!$} 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\boldmath$_M\!\!\!$} is still at most 4.Keywords
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