Optimal Adjacency Labels for Subgraphs of Cartesian Products

06/06/2022

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by   Louis Esperet, et al.

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For any hereditary graph class ℱ, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in ℱ. As a consequence, we show that, if 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 ℱ do too.