New bounds on the minimum density of an identifying code for the infinite hexagonal grid

DOI10.1016/j.dam.2013.06.002zbMath1287.05065arXiv1110.1097OpenAlexW2033439974MaRDI QIDQ2446882

Ari Cukierman, Gexin Yu

Publication date: 23 April 2014

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.1097

zbMATH Keywords

identifying codedischarging methodinfinite hexagonal grid

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graph theory (including graph drawing) in computer science (68R10) Bounds on codes (94B65)

Related Items (11)

Fault tolerant detectors for distinguishing sets in graphs ⋮ Operads of finite posets ⋮ On the minimum size of an identifying code over all orientations of a graph ⋮ Identifying codes for infinite triangular grids with a finite number of rows ⋮ Minimum density of identifying codes of king grids ⋮ Minimum density of identifying codes of king grids ⋮ Locating-Domination and Identification ⋮ Open locating-dominating sets in circulant graphs ⋮ Minimum-Density Identifying Codes in Square Grids ⋮ Open-independent, open-locating-dominating sets ⋮ Optimal open-locating-dominating sets in infinite triangular grids

Cites Work

• Optimal lower bound for 2-identifying codes in the hexagonal grid
• Identification in \(\mathbb Z^2\) using Euclidean balls
• Lower bounds for identifying codes in some infinite grids
• A new lower bound on the density of vertex identifying codes for the infinite hexagonal grid
• Bounds for Codes Identifying Vertices in the Hexagonal Grid
• Improved Bounds forr-Identifying Codes of the Hex Grid
• On a new class of codes for identifying vertices in graphs
• Exact Minimum Density of Codes Identifying Vertices in the Square Grid

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