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arXiv · 2206.02872

Optimal Adjacency Labels for Subgraphs of Cartesian Products

Louis Esperet·Nathaniel Harms·Viktor Zamaraev
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Abstract

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, hashing, and additive combinatorics, and improves upon recent results of Chepoi, Labourel, and Ratel [Journal of Graph Theory, 2020].

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Louis Esperet, Nathaniel Harms, Viktor Zamaraev. 2022-06-06. Optimal Adjacency Labels for Subgraphs of Cartesian Products. https://doi.org/10.1137/23m1587713

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