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arXiv · 2211.07689

Towards the Erdős-Gallai Cycle Decomposition Conjecture

Matija Bucić·Richard Montgomery
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Abstract

In the 1960's, Erdős 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.

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Matija Bucić, Richard Montgomery. 2023-11-14. Towards the Erdős-Gallai Cycle Decomposition Conjecture. https://arxiv.org/abs/2211.07689

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