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- W3172979626 abstract "The binomial random bipartite graph $G(n,n,p)$ is the random graph formed by taking two partition classes of size $n$ and including each edge between them independently with probability $p$. It is known that this model exhibits a similar phase transition as that of the binomial random graph $G(n,p)$ as $p$ passes the critical point of $frac{1}{n}$. We study the component structure of this model near to the critical point. We show that, as with $G(n,p)$, for an appropriate range of $p$ there is a unique `giant' component and we determine asymptotically its order and excess. We also give more precise results for the distribution of the number of components of a fixed order in this range of $p$. These results rely on new bounds for the number of bipartite graphs with a fixed number of vertices and edges, which we also derive." @default.
- W3172979626 created "2021-06-22" @default.
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- W3172979626 date "2021-05-31" @default.
- W3172979626 modified "2023-09-25" @default.
- W3172979626 title "Component behaviour and excess of random bipartite graphs near the critical point" @default.
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- W3172979626 doi "https://doi.org/10.48550/arxiv.2105.14883" @default.
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