Small Implicit Graph Conjecture for hereditary graph classes

A graph class is small if its number of labelled $n$-vertex graphs is at most $n!c^n$ for some constant $c>0$. A class admits an implicit representation if its graphs have adjacency labeling schemes using $O(\log n)$ bits per vertex, where adjacency is determined solely from the labels.

Small Implicit Graph Conjecture. Every hereditary small graph class admits an implicit representation.

This extends the result that every monotone small class admits an information-theoretic order-optimal labeling scheme. The conjecture remains open for hereditary small classes; monotone small classes need not admit information-theoretically asymptotically optimal labeling schemes.