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Results tagged with random-graphs
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user 12705
The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
18
votes
Accepted
Probability, that a graph G does not contain a cycle
I will assume the uniform distribution on all (labelled) graphs with $n$ vertices and $k$ edges. An acyclic graph on $n$ vertices has at most $n-1$ edges, so let me further assume $k< n$. More precise …
- 47.1k
10
votes
Accepted
What is the theory of the random poset?
It is confusing to call this the “random poset”, as it is very different from what is usually called random posets in the literature (in accordance with random graphs): e.g., random posets have height …
- 47.1k
2
votes
zero-one law in bipartite random model $G(n,n,p)$
Yes, by adaptation of the usual proof.
Let $L$ be the first-order language with a unary predicate $P(x)$ (denoting one of the partitions) and $E(x,y)$ (for edges of the graph, directed from $P$ to it …
- 47.1k