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PreprintCC BY 4.0arXiv

Characterisations of Planar Galled Networks

  • Hexuan Liu
  • Taoyang Wu
  • Guan-Ru Yu
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Abstract

Rooted phylogenetic networks are widely used to represent the evolution of species that have undergone reticulate processes. However, these networks can be highly non-planar, making them more difficult to visualise and interpret than evolutionary trees. In this paper, we investigate planarity properties of galled networks, an important subclass of phylogenetic networks. We show that all planar galled networks are necessarily upward planar. Furthermore, by leveraging recent results on planar phylogenetic networks, we provide three characterisations for each of the outerplanar and terminal planar galled network classes in terms of forbidden vertex configurations, forbidden directed subgraphs, and forbidden structures in their associated underlying undirected graphs. These results contribute to a deeper understanding of the structural properties of galled networks and may inform future methods for their construction and visualisation.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026characterisations,
  title = {{Characterisations of Planar Galled Networks}},
  author = {Hexuan Liu and Taoyang Wu and Guan-Ru Yu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.28597},
  eprint = {2609.28597},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28597},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Characterisations of Planar Galled Networks
AU  - Hexuan Liu
AU  - Taoyang Wu
AU  - Guan-Ru Yu
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.28597
UR  - https://arxiv.org/abs/2609.28597
AB  - Rooted phylogenetic networks are widely used to represent the evolution of species that have undergone reticulate processes. However, these networks can be highly non-planar, making them more difficult to visualise and interpret than evolutionary trees. In this paper, we investigate planarity properties of galled networks, an important subclass of phylogenetic networks. We show that all planar galled networks are necessarily upward planar. Furthermore, by leveraging recent results on planar phylogenetic networks, we provide three characterisations for each of the outerplanar and terminal planar galled network classes in terms of forbidden vertex configurations, forbidden directed subgraphs, and forbidden structures in their associated underlying undirected graphs. These results contribute to a deeper understanding of the structural properties of galled networks and may inform future methods for their construction and visualisation.
ER  -