Optimal Adjacency Labels for Subgraphs of Cartesian Products

For any hereditary graph class $\mathcal F$, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $\mathcal F$. As a consequence, we show that, if $\mathcal F$ admits efficient adjacency labels (or, equivalently, small induced-universal graphs) meeting the information-theoretic minimum, then the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $\mathcal F$ do too.