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The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.

11 votes
3 answers
739 views

Rainbow matchings (in random graphs)

Suppose we have an $(n,n)$-bipartite graph with edges colored with $k$ colors. Is anything known about the existence of rainbow matchings (i.e. a matching that uses each color exactly once, for $k=n$) …
Marcin Kotowski's user avatar
8 votes
0 answers
181 views

Can two random graphs be metrically embedded into one another?

Let $X, Y$ be two random graphs on $n$ vertices (say, in $G(n, p)$ model for some $p$). Can anything (expectation, value with high probabiity, ...) be said about $D(X, Y)$, where $D$ is the minimal di …
Marcin Kotowski's user avatar