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2019 Graphs with at most two trees in a forest-building process
Steve Butler, Misa Hamanaka, Marie Hardt
Involve 12(4): 659-670 (2019). DOI: 10.2140/involve.2019.12.659

Abstract

Given a graph, we can form a spanning forest by first sorting the edges in a random order, and then only keeping edges incident to a vertex which is not incident to any previous edge. The resulting forest is dependent on the ordering of the edges, and so we can ask, for example, how likely is it for the process to produce a graph with k trees.

We look at all graphs which can produce at most two trees in this process and determine the probabilities of having either one or two trees. From this we construct infinite families of graphs which are nonisomorphic but produce the same probabilities.

Citation

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Steve Butler. Misa Hamanaka. Marie Hardt. "Graphs with at most two trees in a forest-building process." Involve 12 (4) 659 - 670, 2019. https://doi.org/10.2140/involve.2019.12.659

Information

Received: 30 March 2018; Revised: 10 September 2018; Accepted: 28 October 2018; Published: 2019
First available in Project Euclid: 30 May 2019

zbMATH: 07072545
MathSciNet: MR3941604
Digital Object Identifier: 10.2140/involve.2019.12.659

Subjects:
Primary: 05C05

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 4 • 2019
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