Realization and Connectivity of the Graphs of Origami Flat Foldings
arXiv:1808.06013 · doi:10.20382/jocg.v10i1a10
Abstract
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.
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)