A note on deterministic zombies

Jonathan Narboni,Hoang La,Marthe Bonamy,Laurine Bénéteau,Valentin Bartier

doi:10.1016/j.dam.2021.05.001

A note on deterministic zombies

Jonathan Narboni, Hoang La + Show 3 more

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https://doi.org/10.1016/j.dam.2021.05.001

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Journal: Discrete Applied Mathematics	Publication Date: Jun 1, 2021
Citations: 1	License type: publisher-specific-oa

Affiliation: Institut Polytechnique de Bordeaux, Laboratoire Bordelais de Recherche en Informatique, University of Bordeaux, French National Centre for Scientific Research, University of Montpellier, Montpellier Laboratory of Informatics, Robotics and Microelectronics, Université de Toulon, Aix-Marseille University, Laboratoire d’Informatique et Systèmes, Laboratoire des Sciences pour la Conception, l'Optimisation et la Production, Université Grenoble Alpes

#Cop Number #Multiple Options + Show 8 more

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Abstract

Zombies and Survivor is a variant of the well-studied game of Cops and Robbers where the zombies (cops) can only move closer to the survivor (robber). We consider the deterministic version of the game where a zombie can choose their path if multiple options are available. Similar to the cop number, the zombie number of a graph is the minimum number of zombies required to capture the survivor. In this short note, we solve a question by Fitzpatrick et al., proving that the zombie number of the Cartesian product of two graphs is at most the sum of their zombie numbers. We also give a simple graph family with cop number 2 and an arbitrarily large zombie number.

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