Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed coloring in sparse graphs with fewer colors   This paper is concerned with efficiently coloring sparse graphs in the
distributed setting with as few colors as possible. According to the celebrated
Four Color Theorem, planar graphs can be colored with at most 4 colors, and the
proof gives a (sequential) quadratic algorithm finding such a coloring. A
natural problem is to improve this complexity in the distributed setting. Using
the fact that planar graphs contain linearly many vertices of degree at most 6,
Goldberg, Plotkin, and Shannon obtained a deterministic distributed algorithm
coloring $n$-vertex planar graphs with 7 colors in $O(\log n)$ rounds. Here, we
show how to color planar graphs with 6 colors in $\mbox{polylog}(n)$ rounds.
Our algorithm indeed works more generally in the list-coloring setting and for
sparse graphs (for such graphs we improve by at least one the number of colors
resulting from an efficient algorithm of Barenboim and Elkin, at the expense of
a slightly worst complexity). Our bounds on the number of colors turn out to be
quite sharp in general. Among other results, we show that no distributed
algorithm can color every $n$-vertex planar graph with 4 colors in $o(n)$
rounds.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas