The following theorem is a consequence of Definition 3. The d trapezoid graphs are exactly the cocomparability graphs of partially ordered sets of interval dimension at most d. The properties of MRS s and a direct enumeration method for them are discussed in Section 4. To our knowledge, this question has not been considered before. 1 for an example.
G is a d trapezoid graph if it has a d trapezoid diagram.
The d trapezoid graphs are exactly the cocomparability graphs of partially ordered sets of interval dimension at most d . S. Felsner, R. Mueller and L. Wernisch, Trapezoid graphs and generalizations, geometry and algorithms , Discr.