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The toughness of random graphs
For a connected and non-complete graph $G$ of order $n$, its toughness is defined as \[ τ(G)=\min\bigl\{|S|/c(G-S):S\subseteq V(G),\ c(G-S)>1\bigr\}, \] where $c(G-S)$ denotes the number of components of $G-S$. Let $α(G)$ denote the independence number of $G$. An elementary bound on toughness is $
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