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Poster Abstract
Independence of the Lower Bound for Geometric Triangulation Drawings on the Number of Chains (Poster Abstract)

Authors: Vojtěch Vincíbr, Anežka Kasalová, Zuzana Reiffersová, and Petr Filip

Published in: LIPIcs, Volume 396, 34th International Symposium on Graph Drawing and Network Visualization (GD 2026)


Abstract
In 2026, Cruces, Huemer, and Lara established that a specific combinatorial triangulation can be drawn in at least Ω(3^{n/4}) ways on the double chain as geometric triangulation. We generalize their construction to a d-tuple chain configuration. By introducing the switch subgraph abstraction to count recursive drawing, we obtain the same asymptotic lower bounds Ω(3^{n/4}) ≈ Ω(1.316ⁿ) even when we increase the number of chains.

Cite as

Vojtěch Vincíbr, Anežka Kasalová, Zuzana Reiffersová, and Petr Filip. Independence of the Lower Bound for Geometric Triangulation Drawings on the Number of Chains (Poster Abstract). In 34th International Symposium on Graph Drawing and Network Visualization (GD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 396, pp. 48:1-48:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{vincibr_et_al:LIPIcs.GD.2026.48,
  author =	{Vinc{\'\i}br, Vojt\v{e}ch and Kasalov\'{a}, Ane\v{z}ka and Reiffersov\'{a}, Zuzana and Filip, Petr},
  title =	{{Independence of the Lower Bound for Geometric Triangulation Drawings on the Number of Chains}},
  booktitle =	{34th International Symposium on Graph Drawing and Network Visualization (GD 2026)},
  pages =	{48:1--48:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-452-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{396},
  editor =	{L\"{o}ffler, Maarten and Miksch, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2026.48},
  URN =		{urn:nbn:de:0030-drops-279435},
  doi =		{10.4230/LIPIcs.GD.2026.48},
  annote =	{Keywords: combinatorial triangulation, geometric triangulation, planar graph, d-tuple chain, switch subgraph}
}

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