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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/15360

Title: Flat foldings of plane graphs with prescribed angles and edge lengths
Authors: Abel, Zachary
Demaine, Erik D.
Demaine, Martin L.
Eppstein, David
Lubiw, Anna
Uehara, Ryuhei
Keywords: graph folding
paper folding
graph algorithm
Issue Date: 2018
Publisher: Carleton University, Computational Geometry Laboratory
Magazine name: Journal of Computational Geometry
Volume: 9
Number: 1
Start page: 74
End page: 93
DOI: 10.20382/jocg.v9i1a3
Abstract: When can a plane graph with prescribed edge lengths and prescribed angles (from among {0,180∘,360∘}) be folded flat to lie in an infinitesimally thick line, without crossings? This problem generalizes the classic theory of single-vertex flat origami with prescribed mountain-valley assignment, which corresponds to the case of a cycle graph. We characterize such flat-foldable plane graphs by two obviously necessary but also sufficient conditions, proving a conjecture made in 2001: the angles at each vertex should sum to 360∘, and every face of the graph must itself be flat foldable. This characterization leads to a linear-time algorithm for testing flat foldability of plane graphs with prescribed edge lengths and angles, and a polynomial-time algorithm for counting the number of distinct folded states.
Rights: Copyright (C) 2018 Authors. Zachary Abel, Erik D. Demaine, Martin L. Demaine, David Eppstein, Anna Lubiw, and Ryuhei Uehara, Journal of Computational Geometry, 9(1), 2018, 74-93. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
URI: http://hdl.handle.net/10119/15360
Material Type: publisher
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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