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Cops and Robber on Oriented Graphs with Respect to Push Operation

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Algorithms and Discrete Applied Mathematics (CALDAM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13947))

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Abstract

Graph Searching games are extensively studied in the literature for their vast number of applications in artificial intelligence, robot motion planning, game planning, distributed computing, and graph theory. In particular, Cops and Robber is one of the most well-studied graph searching game, where a set of cops try to capture the position of a single robber. The cop number of a graph is the minimum number of cops required to capture the robber on the graph.

In an oriented graph \(\overrightarrow{G}\), the push operation on a vertex v reverses the orientation of all arcs incident on v. We define and study a variant of the game of Cops and Robber on oriented graphs, where the players also have the ability to push the vertices of the graph.

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Notes

  1. 1.

    An oriented graph is a directed graph without self-loops and 2-cycles.

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Acknowledgement

This research was supported by the IFCAM project “Applications of graph homomorphisms” (MA/IFCAM/18/39).

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Authors and Affiliations

  1. Indian Statistical Institute, Kolkata, India

    Sandip Das & Uma Kant Sahoo

  2. Ben-Gurion University of the Negev, Beer-sheba, Israel

    Harmender Gahlawat

  3. The University of Chicago, Chicago, USA

    Ashwin Ramgopal

  4. Indian Institute of Technology Dharwad, Dharwad, India

    Sagnik Sen

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

Correspondence to Harmender Gahlawat .

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Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India

    Amitabha Bagchi

  2. Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, India

    Rahul Muthu

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Das, S., Gahlawat, H., Ramgopal, A., Sahoo, U.K., Sen, S. (2023). Cops and Robber on Oriented Graphs with Respect to Push Operation. In: Bagchi, A., Muthu, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2023. Lecture Notes in Computer Science, vol 13947. Springer, Cham. https://doi.org/10.1007/978-3-031-25211-2_24

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  • DOI: https://doi.org/10.1007/978-3-031-25211-2_24

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  • Online ISBN: 978-3-031-25211-2

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