Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for the game coloring number of planar graphs with a specific
  girth   Let ${\rm col_g}(G)$ be the game coloring number of a given graph $G.$ Define
the game coloring number of a family of graphs $\mathcal{H}$ as ${\rm
col_g}(\mathcal{H}) := \max\{{\rm col_g}(G):G \in \mathcal{H}\}.$ Let
$\mathcal{P}_k$ be the family of planar graphs of girth at least $k.$ We show
that ${\rm col_g}(\mathcal{P}_7) \leq 5.$ This result extends a result about
the coloring number by Wang and Zhang {WZ11} (${\rm col_g}(\mathcal{P}_8) \leq
5).$ We also show that these bounds are sharp by constructing a graph $G$ where
$G \in {\rm col_g}(\mathcal{P}_k) \geq 5$ for each $k \leq 8$ such that ${\rm
col_g}(G)=5.$ As a consequence, ${\rm col_g}(\mathcal{P}_k) = 5$ for $k =7,8.$

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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas