A forest building process on simple graphs
Combinatorics
2017-09-12 v2
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 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.
Cite
@article{arxiv.1608.00335,
title = {A forest building process on simple graphs},
author = {Zhanar Berikkyzy and Steve Butler and Jay Cummings and Kristin Heysse and Paul Horn and Ruth Luo and Brent Moran},
journal= {arXiv preprint arXiv:1608.00335},
year = {2017}
}