Work

The exact open-locating-dominating density of the kagome grid

Year: 2026

Type: preprint

Abstract: The minimum open-locating-dominating density of the infinite kagome (trihexagonal, hexagon-triangle, 3.6.3.6) grid is 2/5. An explicit periodic construction selects 12 of 30 representative vertices and attains the known universal degree-four lower bound. The finite verifier reconstructs adjacency from shared honeycomb endpoints and checks 360 directed comparisons with absolute-coordinate signatures. The written proof includes the lower counting bound and the infinite-plane density argument.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23978922

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: W7225313185

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