Guang Li

The toughness of random graphs

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