Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumeration of chordal planar graphs and maps   We determine the number of labelled chordal planar graphs with $n$ vertices,
which is asymptotically $c_1\cdot n^{-5/2} \gamma^n n!$ for a constant $c_1>0$
and $\gamma \approx 11.89235$. We also determine the number of rooted simple
chordal planar maps with $n$ edges, which is asymptotically $c_2 n^{-3/2}
\delta^n$, where $\delta = 1/\sigma \approx 6.40375$, and $\sigma$ is an
algebraic number of degree 12. The proofs are based on combinatorial
decompositions and singularity analysis. Chordal planar graphs (or maps) are a
natural example of a subcritical class of graphs in which the class of
3-connected graphs is relatively rich. The 3-connected members are precisely
chordal triangulations, those obtained starting from $K_4$ by repeatedly adding
vertices adjacent to an existing triangular face.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
37
The categories of this paper are: supr-con