bibkey: annor2025domination authors: Dickson Y. B. Annor year: 2025 title: Domination Parameters of Graph Covers doi: 10.48550/arXiv.2502.14341 claim: “Conjecture 14 asserts a universal c > 0 with gamma(G) >= ckgamma(F) for every k-fold graph cover G of F.” strata_touched:

• D5/S3/ConceptDynamics/GraphColoring/AnnorCoverRefutation license: citation-only triage: anchor

Source assertion and bounded search

Original checked: https://arxiv.org/html/2502.14341v2 (2025-11-25), Introduction and Conjecture 14. The exact assertion is:

There exists a constant c>0 such that for every k-fold cover G of a graph F we have gamma(G)>=ckgamma(F).

Mathematical typography is transcribed into ASCII. The following sentence suggests c=3/5; refuting that value alone does not refute Conjecture 14. Graphs are finite, undirected and simple. A covering projection is onto and restricts to a bijection on each open neighborhood. The source explains constant fold for connected bases. It does not require the cover graph to be connected. Domination means every vertex outside the set has a neighbor in the set; its number is the minimum size of such a set.

This source attests the conjecture, not the repository’s refutation. The proof in AnnorCoverRefutation constructs connected bases, positive folds and strict violations for every positive real c. Its literature status is suspected novel after a bounded check, not globally certified.

Search on 2026-09-07 Asia/Singapore (2026-09-06 UTC):

• OpenAlex work W4407806657 and its direct citing-work query recorded zero citations. This is incomplete indexing evidence, not a novelty proof.
• arXiv query all:"Annor" AND all:domination returned the source and arXiv:2506.03646v3. The full latter HTML, dated 2026-06-05, was read: it treats relations among three domination parameters and contains no graph-cover theorem or refutation.
• arXiv searches for perfect codes and graph covers, and OpenAlex searches for "regular graphs" "perfect codes" "covers", were inspected. They recover older perfect-code literature; no inspected result is claimed as a new ingredient. Full citation-forward coverage is absent.
• Direct products of complete graphs have established domination theory: see the separate note vemuri2019domination. The elementary lower bound used here is not claimed new.
• Neumann’s exposition of the common finite covering theorem was read, including the Angluin-Gardiner regular case. Combining that classical result with K_(d+1) already yields covers with perfect codes; see neumann2009on. No novelty is claimed for this existence mechanism.
• The 1975 perfect-code survey retrieval returned HTML, not a PDF, and was not counted as full-text evidence. Broad coding-theory hits do not substitute for a complete citation-forward search.

The stored search responses and preregistrations are in the implementation attempt log referenced by the worker result. Independent mathematical and novelty review remains required before merging or counting a solved problem.

Verified locator

DOI: https://doi.org/10.48550/arXiv.2502.14341. Independently resolved and checked on 2026-09-07 Asia/Singapore against https://arxiv.org/html/2502.14341v2 (2025-11-25), Introduction and Conjecture 14. These locate the finite simple graph-cover conventions and the universal positive-constant conjecture quoted above. The source attests that conjecture, not the repository’s refutation or its novelty.