2023/11/02 by Anthony Bonato, Trent G. Marbach, Bonato, Anthony +5
Decision Sciences · Economics, Econometrics and Finance · #Combinatorics (math.CO) #Economic theories and models #FOS: Mathematics #Game Theory and Applications
paper · pdf · doi:10.48550/arxiv.2311.01582
openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a variant of the Localization game in which the cops have limited visibility, along with the corresponding optimization parameter, the k-visibility localization number ζk, where k is a non-negative integer. We give bounds on k-visibility localization numbers related to domination, maximum degree, and isoperimetric inequalities. For all k, we give a family of trees with unbounded ζk values. Extending results known for the localization number, we show that for k≥ 2, every tree contains a subdivision with ζk = 1. For many n, we give the exact value of ζk for the n × n Cartesian grid graphs, with the remaining cases being one of two values as long as n is sufficiently large. These examples also illustrate that ζi ≠ ζj for all distinct choices of i and j.