Work

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

Year: 2026

Type: preprint

Abstract: Every DET:LD set in the infinite square grid, in the one-false-negative detector model, has lower graph-ball density at least 168/295 at every center. The comparison uses the updated literature interval [12/23,7/12]. The exact minimum remains open. The detector-report condition is checked against the combinatorial criterion. An integer discharging certificate is verified over all 2^25 local patterns, and the analytic argument handles arbitrary plane configurations.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23978918

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: W7225315724

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