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Burning Graphs: A Probabilistic Perspective

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Abstract

In this paper, we study a graph parameter that was recently introduced, the burning number, focusing on a few probabilistic aspects of the problem. The original burning number is revisited and analyzed for binomial random graphs \({\mathcal {G}}(n,p)\), random geometric graphs, and the Cartesian product of paths. Moreover, new variants of the burning number are introduced in which a burning sequence of vertices is selected according to some probabilistic rules. We analyze these new graph parameters for paths.

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Authors and Affiliations

  1. Laboratoire J-A Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice Cedex 02, France

    Dieter Mitsche

  2. Department of Mathematics, Ryerson University, Toronto, ON, Canada

    Paweł Prałat

  3. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada

    Elham Roshanbin

Authors
  1. Dieter Mitsche
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  2. Paweł Prałat
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  3. Elham Roshanbin
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Corresponding author

Correspondence to Dieter Mitsche.

Additional information

D. Mitsche acknowledges support of the PROCOPE-DAAD project RanConGraph (ref. 57134837). P. Prałat acknowledges support from NSERC and Ryerson University.

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Mitsche, D., Prałat, P. & Roshanbin, E. Burning Graphs: A Probabilistic Perspective. Graphs and Combinatorics 33, 449–471 (2017). https://doi.org/10.1007/s00373-017-1768-5

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  • DOI: https://doi.org/10.1007/s00373-017-1768-5

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