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A modification of the random cutting model

Part of: Combinatorial probability Graph theory

Published online by Cambridge University Press:  07 August 2023

Fabian Burghart
Fabian Burghart*
Affiliation:
Uppsala University
*
*Postal address: Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden. Email address: fabian.burghart@math.uu.se
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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 (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.

Keywords

Random cutting modelrandom separation of graphspercolation

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C30: Enumeration in graph theory
Type
Original Article
Information
Advances in Applied Probability , Volume 56 , Issue 1 , March 2024 , pp. 287 - 314
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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