Paper 6. Lower Bounds for the Erdos-Lovasz Cover Number: 3.1108r for Large r

Osman, Mohamed A.

Mohamed A. Osman · ORCID 0009-0004-5912-999X · independent researcher · 2026-10-19

Abstract. We study the incidences between a residual hypergraph of maximum degree three and groups of removed edges chosen as a maximum matching of degree-four blocks. Residual stability, a budget for the matching numbers of witness traces, a rainbow matching theorem of Correia, Pokrovskiy and Sudakov, a recovery step for traces with small matching number, and incidence constraints from exchanges of four-blocks give the proposed bound liminf g(r)/r >= 3.1108, above the constant 3.0534 of Sivashankar (arXiv:2606.24878). The final minimisation is certified with exact rational arithmetic. The combinatorial lemmas are unreviewed.

No priority is claimed for any result, and this is not presented as a settled answer. The lower bound is computer-assisted and has not been independently reviewed by a human or by a proof assistant. AI tools were used throughout the work and its review; every computational claim is regenerated by a script or certified by a proof file in code/ and results/ of the repository. Licence: CC BY 4.0 (text), MIT (code).

Paper 6. Lower Bounds for the Erdos-Lovasz Cover Number: 3.1108r for Large r

A proposed proof that g(r) is asymptotically at least 3.1108r