This repository accompanies Anish Gupta's preprint Tuza's conjecture for graphs of maximum degree at most seven, arXiv:2608.06538 [math.CO].
The paper proves Tuza's triangle packing--covering conjecture for graphs of maximum degree at most seven. Its codegree-four step uses a catalogue of 1,144 machine-checked local certificates; the complete certificate file, generator, and independent verifiers are included here.
- Read the paper on arXiv (or the built PDF in this repository)
- Inspect the certificate catalogue
- See the preferred citation
The programs use exact integer arithmetic and Python's standard library.
make check # fast sharpness and codegree-six checks make check-full # complete codegree-four, -five, and -six suite make paper # three-pass PDF build make sha256 # regenerate the integrity manifest
The computer-assisted catalogue is stated explicitly in the paper; the repository makes that finite step inspectable and reproducible.
Status: preprint, arXiv:2608.06538v1, announced 6 August 2026. The v1 tag
marks the repository state corresponding to that version. This repository is
a public landing page and reproducibility companion; it is not a claim of peer
review.
Software and the Makefile are MIT-licensed. The manuscript, certificate
data, and public documentation are CC BY 4.0; see LICENSES.md.
Contact: Anish Gupta, independent researcher,
ag2269@cantab.ac.uk, ORCID 0009-0008-8137-7729.