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2019 $k$-cut on paths and some trees
Xing Shi Cai, Cecilia Holmgren, Luc Devroye, Fiona Skerman
Electron. J. Probab. 24: 1-22 (2019). DOI: 10.1214/19-EJP318

Abstract

We define the (random) $k$-cut number of a rooted graph to model the difficulty of the destruction of a resilient network. The process is as the cut model of Meir and Moon [21] except now a node must be cut $k$ times before it is destroyed. The first order terms of the expectation and variance of $\mathcal{X} _{n}$, the $k$-cut number of a path of length $n$, are proved. We also show that $\mathcal{X} _{n}$, after rescaling, converges in distribution to a limit $\mathcal{B} _{k}$, which has a complicated representation. The paper then briefly discusses the $k$-cut number of some trees and general graphs. We conclude by some analytic results which may be of interest.

Citation

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Xing Shi Cai. Cecilia Holmgren. Luc Devroye. Fiona Skerman. "$k$-cut on paths and some trees." Electron. J. Probab. 24 1 - 22, 2019. https://doi.org/10.1214/19-EJP318

Information

Received: 9 April 2018; Accepted: 7 May 2019; Published: 2019
First available in Project Euclid: 5 June 2019

zbMATH: 07068784
MathSciNet: MR3968715
Digital Object Identifier: 10.1214/19-EJP318

Subjects:
Primary: 60C05

Keywords: cutting, k-cut, Random trees

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