Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $2$-distance list $(\Delta+2)$-coloring of planar graphs with girth at
  least 10   Given a graph $G$ and a list assignment $L(v)$ for each vertex of $v$ of $G$.
A proper $L$-list-coloring of $G$ is a function that maps every vertex to a
color in $L(v)$ such that no pair of adjacent vertices have the same color. We
say that a graph is list $k$-colorable when every vertex $v$ has a list of
colors of size at least $k$. A $2$-distance coloring is a coloring where
vertices at distance at most 2 cannot share the same color. We prove the
existence of a $2$-distance list ($\Delta+2$)-coloring for planar graphs with
girth at least $10$ and maximum degree $\Delta\geq 4$.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci