Functionality of Random Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915081570222080 |
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| author | Sylvester, John Zamaraev, Viktor Zhukovskii, Maksim |
| author_facet | Sylvester, John Zamaraev, Viktor Zhukovskii, Maksim |
| contents | 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 $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functionality of Random Graphs Sylvester, John Zamaraev, Viktor Zhukovskii, Maksim Combinatorics Discrete Mathematics Probability 05C80, 05C35, 05C69 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 $p$. |
| title | Functionality of Random Graphs |
| topic | Combinatorics Discrete Mathematics Probability 05C80, 05C35, 05C69 |
| url | https://arxiv.org/abs/2412.19771 |