Work

Bounds for dynamic identifying codes in the king grid

Year: 2026

Type: preprint

Abstract: Let M_n count all visits, including repetitions, in a shortest walk whose visited vertices form an identifying code in the n by n king grid. The limit of M_n/n^2 exists and lies between 28/113 and 1/4. For n at least 6, 28n^2/113 - 7n <= M_n <= n^2/4 + 36n. Three exact integer discharging certificates, a walk-cost inequality, and an explicit family of finite walks give the bounds. Connected-set size and repeated-visit walk cost are kept distinct.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23978866

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: W7225316816

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