The Order Dimension of Planar Maps
The Order Dimension of Planar Maps
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平面地图的阶维
DOI：
--
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发表时间：
1997
影响因子：
0.8
通讯作者：
W. T. Trotter
中科院分区：
文献类型：
--
作者：
G. Brightwell;W. T. Trotter
这是一个续集，以前的论文题为凸多面体的顺序尺寸，由相同的作者[SIAM J离散数学，6（1993），pp. 230- 245]。在那篇论文中，我们考虑了偏序集{{\bf P}\protect\boldmath$_M\！$}通过取一个3连通平面映射{\bf M}的顶点、边和面形成，按包含排序，并表明{{\bf P}\protect\boldmath$_M\！$}的序维数总是等于4。本文证明了：如果{\bf M}是任意平面映射，则{{\bf P}\protect\boldmath$_M\！$}的序维数仍然是最多4。
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.