# Improved Distributed Degree Splitting and Edge Coloring

## TL;DR

This paper introduces simpler, faster deterministic distributed algorithms for degree splitting and edge coloring in graphs, achieving smaller discrepancies and improving upon previous methods by Ghaffari and Su.

## Contribution

The authors develop significantly simpler and faster deterministic algorithms for degree splitting and edge coloring, with reduced discrepancy, improving prior work.

## Key findings

- Algorithms are deterministic, simpler, and faster.
- Achieve smaller discrepancy in degree splitting.
- Improve the efficiency of $(2+o(1))\Delta$-edge-coloring.

## Abstract

The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires orienting the edges such that each node has almost the same number of incoming and outgoing edges, again up to a small additive discrepancy. We present deterministic distributed algorithms for both variants, which improve on their counterparts presented by Ghaffari and Su [SODA'17]: our algorithms are significantly simpler and faster, and have a much smaller discrepancy. This also leads to a faster and simpler deterministic algorithm for $(2+o(1))\Delta$-edge-coloring, improving on that of Ghaffari and Su.