Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shorter Labeling Schemes for Planar Graphs   An \emph{adjacency labeling scheme} for a given class of graphs is an
algorithm that for every graph $G$ from the class, assigns bit strings (labels)
to vertices of $G$ so that for any two vertices $u,v$, whether $u$ and $v$ are
adjacent can be determined by a fixed procedure that examines only their
labels. It is known that planar graphs with $n$ vertices admit a labeling
scheme with labels of bit length $(2+o(1))\log{n}$. In this work we improve
this bound by designing a labeling scheme with labels of bit length
$(\frac{4}{3}+o(1))\log{n}$. In graph-theoretical terms, this implies an
explicit construction of a graph on $n^{4/3+o(1)}$ vertices that contains all
planar graphs on $n$ vertices as induced subgraphs, improving the previous best
upper bound of $n^{2+o(1)}$. Our scheme generalizes to graphs of bounded Euler
genus with the same label length up to a second-order term. All the labels of
the input graph can be computed in polynomial time, while adjacency can be
decided from the labels in constant time.

2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys