# Edge-partitioning 3-edge-connected graphs into paths

## TL;DR

This paper proves that sufficiently high minimum degree in 3-edge-connected graphs guarantees an edge-partition into paths of any fixed length, improving previous connectivity requirements.

## Contribution

It establishes the existence of a minimum degree threshold for edge-partitions into paths in 3-edge-connected graphs, refining earlier connectivity bounds.

## Key findings

- Edge-partitions into paths of length l are possible in 3-edge-connected graphs with high minimum degree.
- The minimum degree condition is shown to be optimal, as 2-edge connectivity is insufficient.
- The result generalizes previous work requiring higher edge-connectivity.

## Abstract

We show that for every l, there exists d_l such that every 3-edge-connected graph with minimum degree d_l can be edge-partitioned into paths of length l (provided that its number of edges is divisible by l). This improves a result asserting that 24-edge-connectivity and high minimum degree provides such a partition. This is best possible as 3-edge-connectivity cannot be replaced by 2-edge connectivity.