Planar L-Drawings of Bimodal Graphs

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2022
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Angelini, Patrizio
Chaplick, Steven
Da Lozzo, Giordano
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Journal of Graph Algorithms and Applications. Brown University. 2022, 26(3), pp. 307-334. eISSN 1526-1719. Available under: doi: 10.7155/jgaa.00596
Zusammenfassung

In a planar L-drawing of a directed graph (digraph) each edge e is represented as a polyline composed of a vertical segment starting at the tail of e and a horizontal segment ending at the head of e. Distinct edges may overlap, but not cross. Our main focus is on bimodal graphs, i.e., digraphs admitting a planar embedding in which the incoming and outgoing edges around each vertex are contiguous. We show that every plane bimodal graph without 2-cycles admits a planar L-drawing. This includes the class of upward-plane graphs. Bimodal graphs with 2-cycles admit a planar L-drawing if the underlying undirected graph with merged 2-cycles is a planar 3-tree. Finally, outerplanar digraphs admit a planar L-drawing - although they do not always have a bimodal embedding - but not necessarily with an outerplanar embedding.

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Computational Theory and Mathematics, Geometry and Topology, Computer Science Applications, General Computer Science, Theoretical Computer Science
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ISO 690ANGELINI, Patrizio, Steven CHAPLICK, Sabine CORNELSEN, Giordano DA LOZZO, 2022. Planar L-Drawings of Bimodal Graphs. In: Journal of Graph Algorithms and Applications. Brown University. 2022, 26(3), pp. 307-334. eISSN 1526-1719. Available under: doi: 10.7155/jgaa.00596
BibTex
@article{Angelini2022Plana-68524,
  year={2022},
  doi={10.7155/jgaa.00596},
  title={Planar L-Drawings of Bimodal Graphs},
  number={3},
  volume={26},
  journal={Journal of Graph Algorithms and Applications},
  pages={307--334},
  author={Angelini, Patrizio and Chaplick, Steven and Cornelsen, Sabine and Da Lozzo, Giordano}
}
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