An improved lower bound for error-detecting open-locating-dominating sets in the king grid
Every error-detecting open-locating-dominating set in the infinite king grid has lower graph-ball density at least 79/192 at every center. With the cited upper bound 13/30, this improves the published comparison interval [3/8,13/30]. The exact minimum remains open. An integer transfer table is checked on all 2^25 local assignments, with 13,733,480 admissible patterns. An analytic conservation and boundary argument gives the nonperiodic plane bound.
Authors
- Yasuhito Tsujimura (ORCID: https://orcid.org/0009-0004-9964-9607)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-05
- DOI
- https://doi.org/10.5281/zenodo.23978916
- Primary Topic
- Graph Labeling and Dimension Problems
- Type
- preprint