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Graphs with at
most two trees in a forest-building process
Steve Butler, Misa Hamanaka and Marie Hardt
Vol. 12 (2019), No. 4, 659–670
DOI: 10.2140/involve.2019.12.659
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Abstract |
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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 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. |
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Keywords
forests, edge ordering, components, probability
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Mathematical Subject Classification 2010
Primary: 05C05
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Milestones
Received: 30 March 2018
Revised: 10 September 2018
Accepted: 28 October 2018
Published: 16 April 2019
Communicated by Glenn Hurlbert
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Authors |
| Steve Butler | |
| Department of Mathematics Iowa State University Ames, IA United States |
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| Misa Hamanaka | |
| Department of Mathematics Iowa State University Ames, IA United States |
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| Marie Hardt | |
| Department of Mathematics Iowa State University Ames, IA United States |
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