ℓ $\ell $‐Connectivity and ℓ $\ell $‐edge‐connectivity of random graphs
Ran Gu, Xiaofeng Gu, Yongtang Shi, Hua Wang · Journal of Graph Theory · 2022
Abstract For an integer , the ‐connectivity of a graph is defined to be the minimum number of vertices of whose removal produces a disconnected graph with at least components or a graph with fewer than vertices. The ‐edge‐connectivity of a graph is the minimum number of edges whose removal leaves a graph with at least components if , and if . Given integers and , we investigate and when . Furthermore, our arguments can be used to show that in the random graph process, the hitting times of minimum degree at least and of ‐connectivity (or ‐edge‐connectivity) at least coincide with high probability. These results generalize the work of Bollobás and Thomason on classical connectivity.