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Immunity against Local Influence

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Book cover Language, Culture, Computation. Computing - Theory and Technology

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8001))

Abstract

This paper considers the question of the influence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a graph. A vertex v is said to be controlled by the coalition M if the majority of its neighbors are from M. Let Ruled(G,M) denote the set of vertices controlled by M in G. Previous studies focused on constructions allowing small coalitions to control many vertices, and provided tight bounds for the maximum possible size of Ruled(G,M) (as a function of |M|). This paper introduces the dual problem, concerning the existence and construction of graphs immune to the influence of small coalitions, i.e., graphs G for which Ruled(G,M) is small (relative to |M| again) for every coalition M. Upper and lower bounds are derived on the extent to which such immunity can be achieved.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, The Weizmann Institute, Rehovot, 76100, Israel

    D. Peleg

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  1. D. Peleg
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Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Nachum Dershowitz

  2. Department of Computing, University of London, Goldsmiths College, 25–27 St. James, New Cross, SE14 6NW, London, UK

    Ephraim Nissan

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Peleg, D. (2014). Immunity against Local Influence. In: Dershowitz, N., Nissan, E. (eds) Language, Culture, Computation. Computing - Theory and Technology. Lecture Notes in Computer Science, vol 8001. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45321-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-45321-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45320-5

  • Online ISBN: 978-3-642-45321-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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