%0 Journal Article %1 TROTTER197754 %A Trotter, William T %A Moore, John I %D 1977 %J Journal of Combinatorial Theory, Series B %K dimension linear_extension planar poset %N 1 %P 54 - 67 %R https://doi.org/10.1016/0095-8956(77)90048-X %T The dimension of planar posets %U http://www.sciencedirect.com/science/article/pii/009589567790048X %V 22 %X A partially ordered set (poset) is planar if it has a planar Hasse diagram. The dimension of a bounded planar poset is at most two. We show that the dimension of a planar poset having a greatest lower bound is at most three. We also construct four-dimensional planar posets, but no planar poset with dimension larger than four is known. A poset is called a tree if its Hasse diagram is a tree in the graph-theoretic sense. We show that the dimension of a tree is at most three and give a forbidden subposet characterization of two-dimensional trees.

@article{TROTTER197754, abstract = {A partially ordered set (poset) is planar if it has a planar Hasse diagram. The dimension of a bounded planar poset is at most two. We show that the dimension of a planar poset having a greatest lower bound is at most three. We also construct four-dimensional planar posets, but no planar poset with dimension larger than four is known. A poset is called a tree if its Hasse diagram is a tree in the graph-theoretic sense. We show that the dimension of a tree is at most three and give a forbidden subposet characterization of two-dimensional trees.}, added-at = {2019-06-03T13:06:48.000+0200}, author = {Trotter, William T and Moore, John I}, biburl = {https://www.bibsonomy.org/bibtex/20936270c53383ba29935a208d65e6196/duerrschnabel}, doi = {https://doi.org/10.1016/0095-8956(77)90048-X}, interhash = {8c1c16a6ca400aa40fae6d99a1fba750}, intrahash = {0936270c53383ba29935a208d65e6196}, issn = {0095-8956}, journal = {Journal of Combinatorial Theory, Series B}, keywords = {dimension linear_extension planar poset}, number = 1, pages = {54 - 67}, timestamp = {2019-06-03T13:06:48.000+0200}, title = {The dimension of planar posets}, url = {http://www.sciencedirect.com/science/article/pii/009589567790048X}, volume = 22, year = 1977 }