Sufficient conditions for graphs to be $k$-connected, maximally connected and super-connected

Zhen-Mu Hong, Zheng-Jiang Xia, Fuyuan Chen +1

Let $G$ be a connected graph with minimum degree $\delta (G)$ and vertex-connectivity $\kappa (G)$. The graph $G$ is $k$-connected if $\kappa (G)\ge k$, maximally connected if $\kappa (G)=\delta (G)$, and su…