Realization and Connectivity of the Graphs of Origami Flat Foldings
Realization and Connectivity of the Graphs of Origami Flat Foldings
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折纸平面折叠图的实现及连通性
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
D. Eppstein
中科院分区：
文献类型：
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作者：
D. Eppstein
我们研究的图形形成的顶点和折痕的折纸图案，可以折叠平坦沿着其所有的折痕。正如我们所展示的，这对于一棵树是可能的，当且仅当树的内部顶点都有大于2的偶数度。然而，我们证明（无界纸张，在无穷大的顶点表示所有折痕射线的共享端点）的折叠模式的图形必须是2-顶点连接和4-边连接。
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.