We show that the pathwidth of a cocomparability graph
G equals its treewidth. The proof is based on a new
notion, called interval width, for a partial order
P, which is the smallest width of an interval order
contained in P, and which is shown to be equal to the
treewidth of its cocomparability graph. We observe also
that determining any of these parameters is `cal
NP`-hard and we establish some connections between
classical dimension notions of partial orders and
interval width. In fact we develop approximation
algorithms for interval width of P whose performance
ratios depend on the dimension and interval dimension
of P, respectively.
