Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 4 (2019), 659-670.

Graphs with at most two trees in a forest-building process

Steve Butler, Misa Hamanaka, and Marie Hardt

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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.

Article information

Involve, Volume 12, Number 4 (2019), 659-670.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C05: Trees

forests edge ordering components probability


Butler, Steve; Hamanaka, Misa; Hardt, Marie. Graphs with at most two trees in a forest-building process. Involve 12 (2019), no. 4, 659--670. doi:10.2140/involve.2019.12.659.

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