A forest building process on simple graphs
Zhanar Berikkyzy, Steve Butler, Jay Cummings, Kristin Heysse, Paul, Horn, Ruth Luo, Brent Moran
TL;DR
This paper analyzes a process of building a spanning forest on simple graphs by randomly ordering edges and selecting edges that introduce new vertices, providing formulas for component probabilities and expectations.
Contribution
It introduces a novel process for constructing spanning forests and derives explicit formulas for component probabilities and expected number of components.
Findings
Probability formulas for components in complete bipartite graphs
Expected number of components in any graph
Recurrence relations and basic properties of the process
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.