## 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
^{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.

Originalsprache | englisch |
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Aufsatznummer | P3.7 |

Seitenumfang | 35 |

Fachzeitschrift | Electronic Journal of Combinatorics |

Jahrgang | 30 |

Ausgabenummer | 3 |

DOIs | |

Publikationsstatus | Veröffentlicht - 14 Juli 2023 |

## ASJC Scopus subject areas

- Theoretische Informatik
- Angewandte Mathematik
- Diskrete Mathematik und Kombinatorik
- Geometrie und Topologie
- Theoretische Informatik und Mathematik