Variations of cops and robbers game on grids

Sandip Das; Harmender Gahlawat

doi:10.1007/978-3-319-74180-2_21

Variations of cops and robbers game on grids

Sandip Das, Harmender Gahlawat

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

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 language	English
Title of host publication	Algorithms and Discrete Applied Mathematics - 4th International Conference, CALDAM 2018, Proceedings
Editors	B.S. Panda, Partha P. Goswami
Publisher	Springer Verlag
Pages	249-259
Number of pages	11
ISBN (Print)	9783319741796
DOIs	https://doi.org/10.1007/978-3-319-74180-2_21
State	Published - 1 Jan 2018
Externally published	Yes
Event	4th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2018 - Guwahati, India Duration: 15 Feb 2018 → 17 Feb 2018

Publication series

Name	Communications in Computer and Information Science
Volume	10743 LNCS
ISSN (Print)	1865-0929

Conference

Conference	4th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2018
Country/Territory	India
City	Guwahati
Period	15/02/18 → 17/02/18

ASJC Scopus subject areas

Computer Science (all)
Mathematics (all)

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10.1007/978-3-319-74180-2_21

Cite this

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title = "Variations of cops and robbers game on grids",

abstract = "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{\textquoteright}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.",

author = "Sandip Das and Harmender Gahlawat",

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Das, S & Gahlawat, H 2018, Variations of cops and robbers game on grids. in BS Panda & PP Goswami (eds), Algorithms and Discrete Applied Mathematics - 4th International Conference, CALDAM 2018, Proceedings. Communications in Computer and Information Science, vol. 10743 LNCS, Springer Verlag, pp. 249-259, 4th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2018, Guwahati, India, 15/02/18. https://doi.org/10.1007/978-3-319-74180-2_21

Variations of cops and robbers game on grids. / Das, Sandip; Gahlawat, Harmender.

Algorithms and Discrete Applied Mathematics - 4th International Conference, CALDAM 2018, Proceedings. ed. / B.S. Panda; Partha P. Goswami. Springer Verlag, 2018. p. 249-259 (Communications in Computer and Information Science; Vol. 10743 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Variations of cops and robbers game on grids

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