Here are some inclusions between graph classes that I suspect to hold. In order to include them in ISGCI, they need a (reference to a) nice proof.

outerplanar << EPT

P_4-comparability << co-C_6-free

unipolar << biclique separable

unipolar << interval filament

perfectly orderable << co-sun-free

bip* << (anti-hole,odd-hole)-free

And a question: Is the parameter "book thickness" unbounded for "2-subdivision"?