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arXiv · 1608.00335

A forest building process on simple graphs

Zhanar Berikkyzy·Steve Butler·Jay Cummings·Kristin Heysse·Paul Horn·Ruth Luo·Brent Moran
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Abstract

Consider the following process on a simple graph without isolated vertices: Order the edges randomly and keep an edge if and only if it contains a vertex which is not contained in some preceding edge. The resulting set of edges forms a spanning forest of the graph. The probability of obtaining $k$ components in this process for complete bipartite graphs is determined as well as a formula for the expected number of components in any graph. A generic recurrence and some additional basic properties are discussed.

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Zhanar Berikkyzy, Steve Butler, Jay Cummings, Kristin Heysse, Paul Horn, Ruth Luo, Brent Moran. 2017-09-08. A forest building process on simple graphs. https://arxiv.org/abs/1608.00335

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