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arXiv · 2412.19771

Functionality of Random Graphs

John Sylvester·Viktor Zamaraev·Maksim Zhukovskii
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Abstract

The functionality of a graph $G$ is the minimum number $k$ such that in every induced subgraph of $G$ there exists a vertex whose neighbourhood is uniquely determined by the neighborhoods of at most $k$ other vertices in the subgraph. The functionality parameter was introduced in the context of adjacency labeling schemes, and it generalises a number of classical and recent graph parameters including degeneracy, twin-width, and symmetric difference. We establish the functionality of a random graph $G(n,p)$ up to a constant factor for every value of $p$.

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John Sylvester, Viktor Zamaraev, Maksim Zhukovskii. 2024-12-27. Functionality of Random Graphs. https://arxiv.org/abs/2412.19771

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