Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar Lombardi Drawings for Subcubic Graphs   We prove that every planar graph with maximum degree three has a planar
drawing in which the edges are drawn as circular arcs that meet at equal angles
around every vertex. Our construction is based on the Koebe-Thurston-Andreev
circle packing theorem, and uses a novel type of Voronoi diagram for circle
packings that is invariant under Moebius transformations, defined using
three-dimensional hyperbolic geometry. We also use circle packing to construct
planar Lombardi drawings of a special class of 4-regular planar graphs, the
medial graphs of polyhedral graphs, and we show that not every 4-regular planar
graph has a Lombardi drawing. We have implemented our algorithm for 3-connected
planar cubic graphs.

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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom