Independent Sets in Two-Regular Uniform Hypergraphs
Manuscript 18 October 2026 · Online 18 October 2026
Abstract
For every integer r >= 2, we prove the Balogh-Bollobas-Narayanan independent-set bound for finite simple r-uniform, 2-regular hypergraphs. If such a hypergraph has n vertices, its number of weak independent sets is at most (2^(2(r-1)) + 3(2^(r-1)-1)^2)^(n/(2r)). The proof uses the edge-cover dual and regional entropy inequalities of Sarantis, Tetali and Zheng. An edge-and-odd-cycle factor can be chosen with all its odd cycles induced, by reducing chords. A uniform transfer-matrix estimate handles the remaining closed cycles. This extends the previously stated degree-two cases, odd r and r = 4, to all uniformities without a finite rooted-region enumeration. The general-degree conjecture for d >= 3 is not resolved. This is a self-audited, AI-assisted, unrefereed preprint; no independent review, formal certification or exhaustive priority determination is asserted.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete degree-two bound for all uniformities
- Categories
- math.CO
- Manuscript
- 18 October 2026
- Online release
- 18 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Independent Sets in Two-Regular Uniform Hypergraphs,” EulerSolve Research Papers, OWR-17464-019, 2026. https://doi.org/10.5281/zenodo.23457189.
BibTeX
@misc{ferudun2026tworegularhypergraphs,
author = {Ferudun, Alper},
title = {Independent Sets in Two-Regular Uniform Hypergraphs},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/owr-17464-019/},
doi = {10.5281/zenodo.23457189},
note = {OWR-17464-019; unrefereed preprint}
}