Metraipolis › archive › dc_e2fa838b024e

Encoding level-3 semi-directed phylogenetic networks by quarnets and quinnets — arXiv:2610.07855

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.07855
License (as archived): CC0-1.0
Archived: 2026-10-07T11:53:30.844Z
SHA-256 of the archived text: faf6c1683f24cb0a86c678f890dd2c8ffcc770ea588c209a2276d56e18baa3c9
Stable URL of this page: https://metraipolis.com/documento/dc_e2fa838b024e

How to cite

Encoding level-3 semi-directed phylogenetic networks by quarnets and quinnets — arXiv:2610.07855 — arXiv (en), https://arxiv.org/abs/2610.07855 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e2fa838b024e (Metraipolis archive dc_e2fa838b024e, sha256 faf6c1683f24cb0a86c678f890dd2c8ffcc770ea588c209a2276d56e18baa3c9)

BibTeX

@misc{dce2fa838b024e,
  title = {Encoding level-3 semi-directed phylogenetic networks by quarnets and quinnets — arXiv:2610.07855},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.07855},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e2fa838b024e; sha256 faf6c1683f24cb0a86c678f890dd2c8ffcc770ea588c209a2276d56e18baa3c9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.07855. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Phylogenetic networks generalize phylogenetic trees as models of evolutionary history, allowing lineages to merge as well as to diverge. For many types of genetic data the root position of such a network cannot be recovered, so that only a semi-directed network can be inferred: a mixed graph in which only the edges entering a reticulation vertex are directed. A common strategy for inferring such a network is to first infer the subnetwork it induces on each set of $k\geq 3$ of its leaves, called a $k$-net, and then to assemble these pieces. This can only succeed if the $k$-nets determine the network, in which case that network is said to be encoded by its $k$-nets. Semi-directed networks of level-1 and 2, those whose biconnected components contain at most one, respectively two, reticulations, are known to be encoded by their $4$-nets, or quarnets, whereas level-3 networks are not. Even so, in this paper we show that level-3 semi-directed networks are encoded by their $5$-nets, or quinnets, and we characterize the limitation of quarnets exactly: we show that a single previously reported counterexample captures the only obstruction, every other level-3 network being encoded by its quarnets. Our proofs rest on a collection of encoding results for individual structural features of a network, which we establish for networks of arbitrary level and which are of independent interest.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Populations and Evolution (q-bio.PE) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.07855 — 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 2026-10-07T11:22:09.584Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).