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International Workshop on Combinatorial Algorithms

IWOCA 2019: Combinatorial Algorithms pp 188–200Cite as

Cops and Robber on Some Families of Oriented Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11638))

Abstract

Cops and robber game on a directed graph \(\overrightarrow{D}\) initiates by Player 1 placing k cops and then Player 2 placing one robber on the vertices of \(\overrightarrow{D}\). After that, starting with Player 1, alternately the players may move each of their tokens to the adjacent vertices. Player 1 wins if, after a finite number of moves, a cop and the robber end up on the same vertex and Player 2 wins otherwise. However, depending on the type of moves the players make, there are three different models, namely, the normal cop model: both cops and robber move along the direction of the arcs; the strong cop model: cops can move along or against the direction of the arcs while the robber moves along them; and the weak cop model: the robber can move along or against the direction of the arcs while the cops move along them. A graph is cop-win if Player 1 playing with a single cop has a winning strategy. In this article, we study the three models on some families of oriented graphs and characterize the cop-win directed graphs for the third model.

This work is partially supported by the IFCAM project Applications of graph homomorphisms (MA/IFCAM/18/39).

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Notes

  1. 1.

    GRASTA 2014: http://www-sop.inria.fr/coati/events/grasta2014/.

  2. 2.

    An oriented graph is a directed graph without 2-cycles i.e. each edge has a direction. For the purposes of this article, they are the same.

  3. 3.

    We use the term directed cycle instead of oriented cycle as it is commonly used.

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Author information

Authors and Affiliations

  1. Indian Statistical Institute, Kolkata, India

    Sandip Das, Harmender Gahlawat & Uma Kant Sahoo

  2. Indian Institute of Technology, Dharwad, India

    Sagnik Sen

Authors
  1. Sandip Das
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  2. Harmender Gahlawat
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  3. Uma Kant Sahoo
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  4. Sagnik Sen
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Corresponding author

Correspondence to Harmender Gahlawat .

Editor information

Editors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Charles J. Colbourn

  2. University of Pisa, Pisa, Italy

    Roberto Grossi

  3. University of Pisa, Pisa, Italy

    Nadia Pisanti

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Das, S., Gahlawat, H., Sahoo, U.K., Sen, S. (2019). Cops and Robber on Some Families of Oriented Graphs. In: Colbourn, C., Grossi, R., Pisanti, N. (eds) Combinatorial Algorithms. IWOCA 2019. Lecture Notes in Computer Science(), vol 11638. Springer, Cham. https://doi.org/10.1007/978-3-030-25005-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-25005-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25004-1

  • Online ISBN: 978-3-030-25005-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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