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The One-Cop-Moves Game on Graphs of Small Treewidth

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Combinatorial Optimization and Applications (COCOA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11949))

Abstract

This paper considers the one-cop-moves game played on a graph. In this game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph’s edges with perfect information about each other’s positions. The goal of the cops is to capture the robber. At cops’ turns, exactly one cop is allowed to move from his location to an adjacent vertex; at robber’s turns, she is allowed to move from her location to an adjacent vertex or to stay still. We want to find the minimum number of cops to capture the robber. This number is known as the cop number. In this paper, we investigate the cop number of several classes of graphs, including graphs with treewidth at most 2, Halin graphs, and Cartesian product graphs. We also give a characterization of k-winnable graphs in the one-cop-moves game.

L. Wang—Research supported by a grant for Hong Kong Special Administrative Region, China (CityU 11210119).

B. Yang—Research supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-2018-06800.

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Author information

Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong

    Lusheng Wang

  2. Department of Computer Science, University of Regina, Regina, SK, Canada

    Boting Yang

Authors
  1. Lusheng Wang
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  2. Boting Yang
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Correspondence to Boting Yang .

Editor information

Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Yingshu Li

  2. Florida Atlantic University, Boca Raton, FL, USA

    Mihaela Cardei

  3. Kennesaw State University, Marietta, GA, USA

    Yan Huang

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Wang, L., Yang, B. (2019). The One-Cop-Moves Game on Graphs of Small Treewidth. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_42

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  • DOI: https://doi.org/10.1007/978-3-030-36412-0_42

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36411-3

  • Online ISBN: 978-3-030-36412-0

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