{
  "abstract": "An $st$-orientation of an undirected graph $G$ is an acyclic digraph with a single source $s$ and a single sink $t$ that can be obtained from $G$ by assigning a direction to each edge. The classical problem of deciding if an undirected graph $G$ has an $st$-orientation can be solved efficiently. On the other hand, deciding if an $st$-orientation of $G$ exists that does not have any transitive arc is NP-complete, even if each vertex of $G$ has degree at most four. Here we show that this last decision problem remains NP-complete if $G$ is cubic, which settles an open question by Binucci et al. (2025). We obtain NP-completeness for two variants of the problem: (i) $s$ and $t$ are fixed and given as part of the input and (ii) $s$ and $t$ can be chosen freely. We then use these results to investigate the computational complexity of a problem that arises in computational evolution. Specifically, we show that the problem of deciding if an unrooted binary phylogenetic network has an orientation as a rooted binary phylogenetic network without any shortcuts (the analog of a transitive arcs in phylogenetics) is NP-complete. Our results connect the two (mostly) distinct research areas of orienting undirected graphs and orienting unrooted phylogenetic networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28654",
  "author_total": 2,
  "authors": [
    {
      "name": "Janosch Döcker"
    },
    {
      "name": "Simone Linz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40vg00xp2yw1b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28654",
  "fulltext_url": null,
  "id": "40vg00xp2yw1b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28654",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7204880556",
  "pdf_url": "https://arxiv.org/pdf/2608.28654",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40vg00xp2yw1b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28654",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28654"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Orientations without transitive arcs for cubic graphs and phylogenetic networks",
  "title_text": "Orientations without transitive arcs for cubic graphs and phylogenetic networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:49Z",
  "url": "https://research.draconitic.com/paper/40vg00xp2yw1b",
  "venue": "arXiv",
  "versions": []
}