The Matching Process and Independent Process in Random Regular Graphs and Hypergraphs
Combinatorics
2021-09-24 v2
Abstract
In this note, we analyze two random greedy processes on sparse random graphs and hypergraphs with a given degree sequence. First we analyze the matching process, which builds a set of disjoint edges one edge at a time; then we analyze the independent process, which builds an independent set of vertices one vertex at a time. We use the differential equations method and apply a general theorem of Warnke. Our main contribution is to significantly reduce the associated systems of differential equations and simplify the expression for the final size of the matching or independent set.
Cite
@article{arxiv.1603.09232,
title = {The Matching Process and Independent Process in Random Regular Graphs and Hypergraphs},
author = {Deepak Bal and Patrick Bennett},
journal= {arXiv preprint arXiv:1603.09232},
year = {2021}
}
Comments
27 pages. This version adds results about the independent process and generalizes previous results to degree sequences which may depend on $n$