A characterization of terminal planar networks by forbidden structures
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.
Keywords
Cite
@article{arxiv.2603.16657,
title = {A characterization of terminal planar networks by forbidden structures},
author = {Haruki Miyaji and Yuki Noguchi and Hexuan Liu and Takatora Suzuki and Keita Watanabe and Taoyang Wu and Momoko Hayamizu},
journal= {arXiv preprint arXiv:2603.16657},
year = {2026}
}
Comments
29 pages, 12 figures