Towards the Erdős-Gallai cycle decomposition conjecture

In the 1960's, Erdos and Gallai conjectured that the edges of any n-vertex graph can be decomposed into O(n) cycles and edges. We improve upon the previous best bound of O(n log log n) cycles and edges due to Conlon, Fox and Sudakov, by showing an n-vertex graph can always be decomposed into O(n log* n) cycles and edges, where log* n is the iterated logarithm function.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This article improves upon previous research by showing that any n-vertex graph can be decomposed into O(n log* n) cycles and edges.