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

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
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preprint

An improved lower bound for error-detecting open-locating-dominating sets in the king grid

Yasuhito Tsujimura
Zenodo (CERN European Organization for Nuclear Research)
Graph Labeling and Dimension Problems
preprint

An improved lower bound for error-detecting open-locating-dominating sets in the king grid

Yasuhito Tsujimura
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Graph Labeling and Dimension Problems
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An improved lower bound for error-detecting open-locating-dominating sets in the king grid — Yasuhito Tsujimura · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS