Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar Octilinear Drawings with One Bend Per Edge   In octilinear drawings of planar graphs, every edge is drawn as an
alternating sequence of horizontal, vertical and diagonal ($45^\circ$)
line-segments. In this paper, we study octilinear drawings of low edge
complexity, i.e., with few bends per edge. A $k$-planar graph is a planar graph
in which each vertex has degree less or equal to $k$. In particular, we prove
that every 4-planar graph admits a planar octilinear drawing with at most one
bend per edge on an integer grid of size $O(n^2) \times O(n)$. For 5-planar
graphs, we prove that one bend per edge still suffices in order to construct
planar octilinear drawings, but in super-polynomial area. However, for 6-planar
graphs we give a class of graphs whose planar octilinear drawings require at
least two bends per edge.

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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ