# [A linear cycle-and-edge decomposition of every graph](main.pdf)

**Author:** OpenAI

**Date:** September 24, 2026

## Citation

To cite this manuscript:

```bibtex
@misc{OAI:A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026,
  author = {{OpenAI}},
  title = {{A linear cycle-and-edge decomposition of every graph}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026/main.pdf}{OAI:A-linear-cycle-and-edge-decomposition-of-every-graph-September-24-2026}},
  year = {2026}
}
```