Asymptotics for the number of bipartite graphs with fixed surplus
Combinatorics
2024-11-15 v1 Probability
Abstract
In a recent work on the bipartite Erd\H{o}s-R\'{e}nyi graph, Do et al. (2023) established upper bounds on the number of connected labeled bipartite graphs with a fixed surplus. We use some recent encodings of bipartite random graphs in order to provide a probabilistic formula for the number of bipartite graphs with fixed surplus. Using this, we obtain asymptotics as the number of vertices in each class tend to infinity.
Keywords
Cite
@article{arxiv.2411.09419,
title = {Asymptotics for the number of bipartite graphs with fixed surplus},
author = {David Clancy},
journal= {arXiv preprint arXiv:2411.09419},
year = {2024}
}
Comments
15 pages, 2 figures