Let G = (V, E) be an undirected, unweighted graph with n = |V | vertices. The distance between two vertices u, v
∈ G is the length of the shortest path between them. A vertex cut of G is a subset S ⊆ V such that removing the vertices in S (as well as incident edges) disconnects G.
Show that if there exist u, v ∈ G of distance d > 1 from each other, that there exists a vertex cut of size at most (n − 2)/(d − 1). Assume G is connected.
I tried induction, but the inductive step seems to be a bit messy. What other proof approaches would work?
Recently Asked Questions
- Describe the main features of three most popular public IaaS clouds. Only the most prominent and distinguishing features of each one of them are to be
- Not quite too sure about this
- In the current business environment, which of the four cloud computing service models (infrastructure as a service (IaaS), platform as a service (PaaS),