adding vertex to spanning tree

Question

Suppose graph G has minimum spanning tree computed.How  quickly can we update minimum spanning tree if we add new vertex and incident edges to G?

Answer 1

T.C is O(VlogV)  following screenshot is taken from solution manual of Coreman's book:

Answer 2

Adding vertex  and incident edges to minimum.spanning tree we get a graph.Check for cycles in graph and remove max edge from each  cycle..this will give new spanning tree

Comments

Can you please explain what is the meaning of this statement :

How  quickly can we update minimum spanning tree if we add new vertex and incident edges to G?