Variations of cops and robbers game on grids

Sandip Das, Harmender Gahlawat

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


Cops and robber is a two player turn based game played on a graph where the cops try to catch the robber. The cop number of a graph is the minimum number of cops required to catch the robber. We consider two variants of this game, namely cops and attacking robber, and lazy cops and robber. In cops and attacking robber, the robber can attack a cop and remove him from the game, whereas in lazy cops and robber only one cop is allowed to move during the cop’s turn. We prove that the cop number for both these variants in finite square grids is two. We show that the cop number for cops and attacking robber in n-dimensional hypercube is at most n, and the cop number in the same version of a 3-dimensional grid is three.

Original languageEnglish
Title of host publicationAlgorithms and Discrete Applied Mathematics - 4th International Conference, CALDAM 2018, Proceedings
EditorsB.S. Panda, Partha P. Goswami
PublisherSpringer Verlag
Number of pages11
ISBN (Print)9783319741796
StatePublished - 1 Jan 2018
Externally publishedYes
Event4th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2018 - Guwahati, India
Duration: 15 Feb 201817 Feb 2018

Publication series

NameCommunications in Computer and Information Science
Volume10743 LNCS
ISSN (Print)1865-0929


Conference4th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2018

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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