A playful note on spanning and surplus edges
Probability
2017-03-09 v1 Combinatorics
Abstract
Consider a (not necessarily near-critical) random graph running in continuous time. A recent breadth-first-walk construction is extended in order to account for the surplus edge data in addition to the spanning edge data. Two different graph representations of the multiplicative coalescent, with different advantages and drawbacks, are discussed in detail. A canonical multi-graph of Bhamidi, Budhiraja and Wang (2014) naturally emerges. The presented framework should facilitate understanding of scaling limits with surplus edges for near-critical random graphs in the domain of attraction of general (not necessarily standard) eternal multiplicative coalescent.
Cite
@article{arxiv.1703.02574,
title = {A playful note on spanning and surplus edges},
author = {Vlada Limic},
journal= {arXiv preprint arXiv:1703.02574},
year = {2017}
}
Comments
13 pages, 7 figures