We investigate the graphs formed from the vertices and creases of an origami pattern that can be folded flat along all of its creases. As we show, this is possible for a tree if and only if the internal vertices of the tree all have even degree greater than two. However, we prove that (for unbounded sheets of paper, with a vertex at infinity representing a shared endpoint of all creased rays) the graph of a folding pattern must be 2-vertex-connected and 4-edge-connected.
@article{arxiv.1808.06013,
title = {Realization and Connectivity of the Graphs of Origami Flat Foldings},
author = {David Eppstein},
journal= {arXiv preprint arXiv:1808.06013},
year = {2019}
}
Comments
24 pages, 12 figures. To appear (without the appendices) in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)