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Media Exposition
Visualizing Lucas’s Hamiltonian Paths Through the Associahedron 1-Skeleton (Media Exposition)

Authors: Kacey Thien-Huu La, Jose E. Arbelo, and Christopher J. Tralie

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)


Abstract
We re-examine the 1987 paper by Joan Lucas[Lucas, 1987], who showed that the edge-flip graph of convex polygon triangulations is Hamiltonian. We focus specifically on the first part of her paper on Hamiltonian paths, and we provide a simplified algorithm for that case which elucidates how to assemble a recursive subdivision that she refers to as "stacks." Finally, we provide an interactive web-based visualization of Hamiltonian paths through the stacks.

Cite as

Kacey Thien-Huu La, Jose E. Arbelo, and Christopher J. Tralie. Visualizing Lucas’s Hamiltonian Paths Through the Associahedron 1-Skeleton (Media Exposition). In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 90:1-90:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{la_et_al:LIPIcs.SoCG.2024.90,
  author =	{La, Kacey Thien-Huu and Arbelo, Jose E. and Tralie, Christopher J.},
  title =	{{Visualizing Lucas’s Hamiltonian Paths Through the Associahedron 1-Skeleton}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{90:1--90:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.90},
  URN =		{urn:nbn:de:0030-drops-200355},
  doi =		{10.4230/LIPIcs.SoCG.2024.90},
  annote =	{Keywords: associahedron, hamiltonian paths, visualization, tree rotations, convex polygons}
}