How many edges before a random graph is connected?
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04-11-2019 - |
Pergunta
Let $G$ be a undirected graph with $n$ vertices and no edges, and let $f(k)$ be the probability that if we add $k$ edges randomly to $G$ that $G$ will be connected. How would one determine $f(k)$ for a given $n\in\mathbb N$?
Specifics:
When we add an edge to the graph $G$, any edge that can exist would be equally likely to be added. We can not add the same edge twice, so when $k=\frac{n^2+n}2$ (the number of possible edges in a graph with $n$ verticies), then $f(k)=1$.
Definition for connected may be found on wikipedia.
Nenhuma solução correta
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