Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realization and Connectivity of the Graphs of Origami Flat Foldings   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.

35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph