bibkey: fernandezetal2025weakmetric
authors: Elena Fernandez; Sandi Klavzar; Dorota Kuziak; Manuel Munoz-Marquez; Ismael G. Yero
year: 2025
title: On the weak k-metric dimension of Hamming graphs
doi: 10.1016/j.disopt.2026.100945
url: https://arxiv.org/abs/2505.19642
claim: "The introduction gives the weak one-metric dimension of K_n square K_n; Theorem 1.1 gives the weak two-metric dimension."
strata_touched:
  - D5/S3/Combinatorics/Hamming/TernaryWeakMetricStability
license: citation-only
triage: anchor

Published square-product boundary values

The primary source is arXiv:2505.19642v1, 26 May 2025. Its submission history was checked on 28 October 2026 and lists v1. The introduction states wdim_1(K_n square K_n) = floor((4n-2)/3). The k=2 line of Theorem 1.1 gives wdim_2(K_n square K_n) = ceil(4n/3) for n >= 3.

At n=3 these are 3 and 4. They are exactly the d=2 boundary values for the ternary deficits t=5 and t=4, since kappa(2)=6. They receive no novelty credit. Their role in the retained threshold theorem is to rule out every cutoff at most two; the three-landmark L and four-corner square realize the values.

Verified locator

DOI: https://doi.org/10.1016/j.disopt.2026.100945

Source: https://arxiv.org/abs/2505.19642

The introduction and Theorem 1.1 locate the weak one-metric and weak two-metric square-product values described above.