Let $(P,\leq)$ be a finit poset, $w$ its width. Then, by Dilworth's theorem, I know that $P$ is a union of $w$ chains.
My question is: is there also a relation between the order dimension of a poset and its width?
Thanks very much for the help. Also if there are any results that some how disciplines the order dimension of a poset based on any order relation's properties it would be of great help.