平面有盖网络的刻画
Characterisations of Planar Galled Networks
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中文总结 AI 辅助
本文研究有盖网络的平面性，证明所有平面有盖网络必为向上平面，并基于禁止结构为外平面和终端平面有盖网络提供三种刻画，深化结构理解并助力可视化。
中文摘要 AI 辅助
有根系统发育网络被广泛用于表示经历了网状过程的物种进化。然而，这些网络可能高度非平面，使其比进化树更难以可视化和解释。在本文中，我们研究了有盖网络的平面性性质，这是系统发育网络的一个重要子类。我们证明了所有平面有盖网络必然是向上平面的。此外，通过利用近期关于平面系统发育网络的结果，我们为外平面和终端平面有盖网络类各提供了三种刻画，分别基于禁止顶点配置、禁止有向子图及其相关底层无向图中的禁止结构。这些结果有助于更深入地理解有盖网络的结构性质，并可能为未来构建和可视化这些网络的方法提供参考。
英文摘要
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.
发表机构
- Waseda University（早稻田大学）
- University of East Anglia（东英吉利大学）
- National Sun Yat-sen University（国立中山大学）
机构由 AI 辅助整理，请以论文原文为准。
