Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superpatterns and Universal Point Sets   An old open problem in graph drawing asks for the size of a universal point
set, a set of points that can be used as vertices for straight-line drawings of
all n-vertex planar graphs. We connect this problem to the theory of
permutation patterns, where another open problem concerns the size of
superpatterns, permutations that contain all patterns of a given size. We
generalize superpatterns to classes of permutations determined by forbidden
patterns, and we construct superpatterns of size n^2/4 + Theta(n) for the
213-avoiding permutations, half the size of known superpatterns for
unconstrained permutations. We use our superpatterns to construct universal
point sets of size n^2/4 - Theta(n), smaller than the previous bound by a 9/16
factor. We prove that every proper subclass of the 213-avoiding permutations
has superpatterns of size O(n log^O(1) n), which we use to prove that the
planar graphs of bounded pathwidth have near-linear universal point sets.

20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
28
The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: solv-int