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A Modification of the Random Cutting Model

Author Fabian Burghart

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Author Details

Fabian Burghart
  • Department of Mathematics, Uppsala University, Sweden

Funding

Partially supported by grants from the Knut and Alice Wallenberg Foundation, the Ragnar Söderberg Foundation, and the Swedish Research Council.

Acknowledgements

The author wishes to thank his academic advisors, Cecilia Holmgren and Svante Janson, for their generous support and many helpful remarks and discussions. The author also wishes to thank the anonymous referees for their helpful comments.

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Fabian Burghart. A Modification of the Random Cutting Model. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.AofA.2022.4

Abstract

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 [Meir and Moon, 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 complete binary trees.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic algorithms
Keywords
  • Random cutting model
  • Random separation of graphs
  • Percolation

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