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1 results

  • A modification of the random cutting model

  • Part of
  • Fabian Burghart
  • Journal:
    Advances in Applied Probability / Volume 56 / Issue 1 / March 2024
    Published online by Cambridge University Press:
    07 August 2023, pp. 287-314
    Print publication:
    March 2024
    • Article
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  • We propose a modification to the random destruction of graphs: given a finite network with a distinguished set of sources and targets, remove (cut) vertices at random, discarding components that do not contain a source node. We investigate the number of cuts required until all targets are removed, and the size of the remaining graph. This model interpolates between the random cutting model going back to Meir and Moon (J. Austral. Math. Soc. 11, 1970) and site percolation. We prove several general results, including that the size of the remaining graph is a tight family of random variables for compatible sequences of expander-type graphs, and determine limiting distributions for binary caterpillar trees and complete binary trees.