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arXiv · 2603.16657

A characterization of terminal planar networks by forbidden structures

Haruki Miyaji·Yuki Noguchi·Hexuan Liu·Takatora Suzuki·Keita Watanabe·Taoyang Wu·Momoko Hayamizu
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Abstract

The class of terminal planar networks was recently introduced from a biological perspective in relation to the visualization of phylogenetic networks, and its connection to upward planar networks has been established. We provide a Kuratowski-type theorem that characterizes terminal planar networks by a finite set of forbidden structures, defined via six families of 0/1-labeled graphs. Another characterization based on planarity of supergraphs yields linear-time algorithms for testing terminal planarity and for computing such planar drawings. We describe an application that is potentially relevant in broader, non-phylogenetic settings. We also discuss a connection of our main result to an open problem on the forbidden structures of single-source upward planar networks.

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Haruki Miyaji, Yuki Noguchi, Hexuan Liu, Takatora Suzuki, Keita Watanabe, Taoyang Wu, Momoko Hayamizu. 2026-03-17. A characterization of terminal planar networks by forbidden structures. https://arxiv.org/abs/2603.16657

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