However, a non-triangular odd cycle is never a comparability graph.
i3 : G = graph {{1,2}, {2,3}, {3,4}, {4,5}, {1,5}};
i4 : isComparabilityGraph G
o4 = false
This method calls transitiveOrientation and checks that an error is not thrown. See the documentation for that method for a note on the implemented algorithm.