What type of study is this?

This is a Experimental Study study.

September 27, 2025Open Access

A New Variant of the Localization Game

Key Points

The introduction of a variant where distance probes reveal only distances of 0 or 1 changes game dynamics significantly.
A single cop can effectively capture the robber on certain graphs, showcasing unique characteristics of the modified game.
The study extensively examines trees and planar graphs, indicating the variant's drastic differences from the original game.
A relaxed version of the variant aids in establishing search bounds, enhancing understanding of the game.

Abstract

In the Localization game, a set of cops use distance probes to attempt to capture an invisible robber on a graph. The present work introduces a variant in which these probes are restricted to reveal only distances of 0 or 1. This is explored for general graphs, planar graphs, and extensively for trees, on which the variant is drastically different from the original game. A characterization is given of all graphs on which a single cop can win the modified game. We also introduce a relaxed version of the variant, which is found to be particularly useful in the search for bounds.

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Cite This Study

Michael Molnar (Thu,) studied this question.

synapsesocial.com/papers/68d7b3e2eebfec0fc5236b6b https://doi.org/https://doi.org/10.32920/30203425

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