Work

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

Year: 2026

Type: preprint

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.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23978916

Author: Tsujimura, Yasuhito

Language: English

Topic: Graph Labeling and Dimension Problems

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225346767

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