The localization capture time of a graph

05/20/2021
by   Natalie C. Behague, et al.
0

The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the location of the robber. We present a novel graph parameter called the capture time, which measures how long the localization game lasts assuming optimal play. We conjecture that the capture time is linear in the order of the graph, and show that the conjecture holds for graph families such as trees and interval graphs. We study bounds on the capture time for trees and its monotone property on induced subgraphs of trees and more general graphs. We give upper bounds for the capture time on the incidence graphs of projective planes. We finish with new bounds on the localization number and capture time using treewidth.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/13/2018

Bounds on the localization number

We consider the localization game played on graphs, wherein a set of cop...
research
09/18/2017

Localization game on geometric and planar graphs

The main topic of this paper is motivated by a localization problem in c...
research
08/23/2017

Limited Visibility Cops and Robbers

We consider a variation of the Cops and Robber game where the cops can o...
research
07/05/2023

Locating Robber with Cop Strategy Graph: Subdivision vs. Multiple Cop

We consider the Robber Locating Game, where an invisible moving robber t...
research
05/26/2020

The localization number of designs

We study the localization number of incidence graphs of designs. In the ...
research
01/09/2023

The one-visibility Localization game

We introduce a variant of the Localization game in which the cops only h...
research
10/26/2022

Optimal Patrolling Strategies for Trees and Complete Networks

We present solutions to a continuous patrolling game played on network. ...

Please sign up or login with your details

Forgot password? Click here to reset