Comparability graphs and intersection graphs

A function diagram (f-diagram) D consists of the family of curves {i, . . . , ii} obtained from n continuous functions fi : [O, 1] -B R (1 G i d n). We call the intersection graph of D a function graph (f-graph). It is shown that a graph G is an f-graph if and only if its complement 0 is a comparability graph. An f-diagram generalizes the notion cf a permutation diagram where the fi are linear f*mctions. It is also shown that G is the intersection graph of the concatenation of &c permutation diagrams if and only if the partial order dimension of e is ak t 1. Computational complexity results are obtained for recognizing such graphs.