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For a simple, connected graph, we consider the forest building process in which all edges are randomly ordered, and an edge is kept in the reconstruction if and only if it is incident to at least one vertex which is not incident to any preceding edges. The resulting spanning forest is characterized by a number of trees or components, and we prescribe a general formula for the number of permutations producing any number k components on a path Pn. We similarly present formulas for the number of permutations producing exactly 1 component on graph families including brooms, spiders, and lassos.
Hiveley, Aurora, "A Forest Building Process on Graph Families" (2023). Mathematics, Statistics, and Computer Science Honors Projects. 74.
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