Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the strong chromatic number of graphs   The strong chromatic number, $\chi_S(G)$, of an $n$-vertex graph $G$ is the
smallest number $k$ such that after adding $k\lceil n/k\rceil-n$ isolated
vertices to $G$ and considering {\bf any} partition of the vertices of the
resulting graph into disjoint subsets $V_1, \ldots, V_{\lceil n/k\rceil}$ of
size $k$ each, one can find a proper $k$-vertex-coloring of the graph such that
each part $V_i$, $i=1, \ldots, \lceil n/k\rceil$, contains exactly one vertex
of each color.
  For any graph $G$ with maximum degree $\Delta$, it is easy to see that
$\chi_S(G)\geq\Delta+1$. Recently, Haxell proved that $\chi_S(G) \leq 3\Delta
-1$. In this paper, we improve this bound for graphs with large maximum degree.
We show that $\chi_S(G)\leq 2\Delta$ if $\Delta \geq n/6$ and prove that this
bound is sharp.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex