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Adjacency Labeling Schemes of Size $\log n+O(\log\log^* n)$ for Graphs of Bounded Treewidth — arXiv:2611.03620

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03620
License (as archived): CC0-1.0
Archived: 2026-11-03T11:45:50.631Z
SHA-256 of the archived text: c45fa6375b8449d2f851bc5d1aaeb430e7a3f3d5f2b74f36b1741468a4c4a85f
Stable URL of this page: https://metraipolis.com/documento/dc_c4e6817fa486

How to cite

Adjacency Labeling Schemes of Size $\log n+O(\log\log^* n)$ for Graphs of Bounded Treewidth — arXiv:2611.03620 — arXiv (en), https://arxiv.org/abs/2611.03620 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c4e6817fa486 (Metraipolis archive dc_c4e6817fa486, sha256 c45fa6375b8449d2f851bc5d1aaeb430e7a3f3d5f2b74f36b1741468a4c4a85f)

BibTeX

@misc{dcc4e6817fa486,
  title = {Adjacency Labeling Schemes of Size $log n+O(loglog^* n)$ for Graphs of Bounded Treewidth — arXiv:2611.03620},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03620},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c4e6817fa486; sha256 c45fa6375b8449d2f851bc5d1aaeb430e7a3f3d5f2b74f36b1741468a4c4a85f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03620. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Gavoille and Labourel (ESA 2007) gave an adjacency labeling scheme of size $\log n+O(k\log\log n)$ for graphs of treewidth at most $k$, and asked whether $\log n+O(k)$ bits suffice. We give a labeling scheme of size $\log n+O(\log\log^* n)$ for every fixed $k$, the first improvement of the second-order term for any $k\ge 2$. Equivalently, there is an induced-universal graph with $n(\log^* n)^{O_k(1)}$ vertices for this family. We work with laminar families of intervals, in which a vertex finds each earlier neighbor as the owner of an interval of a given nesting depth around it. As long as every subtree occupies consecutive positions, the nesting depth must be logarithmic, and $\log\log n$ bits per neighbor follow. We give up contiguity. Heavy subtrees are moved out, which brings the depth down to $O(\log^* n)$; the intervals broken by the moves are repaired with $2^{O(k^3)}$ additional intervals per vertex; and the bits needed to find these intervals are paid for by the moved subtrees.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv cs.DS, nuovi lavori del giorno).
Categorie arXiv: Data Structures and Algorithms (cs.DS) ; Discrete Mathematics (cs.DM).
Pagina del lavoro: https://arxiv.org/abs/2611.03620 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:07:52.266Z dalla pagina https://arxiv.org/list/cs.DS/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).