The dimension of planar posets
作者： William T Trotter , John I Moore
DOI: 10.1016/0095-8956(77)90048-X
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摘要: Abstract A partially ordered set (poset) is planar if it has a Hasse diagram. The dimension of bounded poset at most two. We show that the having greatest lower bound three. also construct four-dimensional posets, but no with larger than four known. called tree its diagram in graph-theoretic sense. three and give forbidden subposet characterization two-dimensional trees.
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sci-hub.se 参考文章(11)
Toshio Hiraguchi, On the Dimension of Orders The science reports of the Kanazawa University＝金沢大学理科報告. ,vol. 4, pp. 1- 20 ,(1955)
Edward Szpilrajn, Sur l'extension de l'ordre partiel Fundamenta Mathematicae. ,vol. 16, pp. 386- 389 ,(1930) , 10.4064/FM-16-1-386-389
William T. Trotter, John I. Moore, Some theorems on graphs and posets Discrete Mathematics. ,vol. 15, pp. 79- 84 ,(1976) , 10.1016/0012-365X(76)90111-4
William T. Trotter, Dimension of the crown Skn Discrete Mathematics. ,vol. 8, pp. 85- 103 ,(1974) , 10.1016/0012-365X(74)90113-7
E. S. Wolk, A note on “The comparability graph of a tree” Proceedings of the American Mathematical Society. ,vol. 16, pp. 17- 20 ,(1965) , 10.1090/S0002-9939-1965-0172274-5
William T. Trotter, Kenneth P. Bogart, On the complexity of posets Discrete Mathematics. ,vol. 16, pp. 71- 82 ,(1976) , 10.1016/0012-365X(76)90095-9
R. P. Dilworth, A Decomposition Theorem for Partially Ordered Sets Classic Papers in Combinatorics. ,vol. 51, pp. 139- 144 ,(2009) , 10.1007/978-0-8176-4842-8_10
William T. Trotter, Inequalities in dimension theory for posets Proceedings of the American Mathematical Society. ,vol. 47, pp. 311- 316 ,(1975) , 10.1090/S0002-9939-1975-0369192-2
Mary Ellen Rudin, Souslin's Conjecture American Mathematical Monthly. ,vol. 76, pp. 1113- 1119 ,(1969) , 10.1080/00029890.1969.12000425
Ben Dushnik, E. W. Miller, Partially Ordered Sets American Journal of Mathematics. ,vol. 63, pp. 600- ,(1941) , 10.2307/2371374