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. Our proof uses ideas from randomized communication complexity and hashing, and improves upon recent results of Chepoi, Labourel, and Ratel [Journal of Graph Theory, 2020].
@InProceedings{esperet_et_al:LIPIcs.ICALP.2023.57, author = {Esperet, Louis and Harms, Nathaniel and Zamaraev, Viktor}, title = {{Optimal Adjacency Labels for Subgraphs of Cartesian Products}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {57:1--57:11}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.57}, URN = {urn:nbn:de:0030-drops-181093}, doi = {10.4230/LIPIcs.ICALP.2023.57}, annote = {Keywords: Adjacency labeling schemes, Cartesian product, Hypercubes} }
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