Asymptotics for the number of bipartite graphs with fixed surplus
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912118886891520 |
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| author | Clancy Jr, David |
| author_facet | Clancy Jr, David |
| contents | In a recent work on the bipartite Erdős-Rényi 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09419 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics for the number of bipartite graphs with fixed surplus Clancy Jr, David Combinatorics Probability 05C30, 60C05 In a recent work on the bipartite Erdős-Rényi 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. |
| title | Asymptotics for the number of bipartite graphs with fixed surplus |
| topic | Combinatorics Probability 05C30, 60C05 |
| url | https://arxiv.org/abs/2411.09419 |