HELP

I think this was asked a week ago. The OP perhaps deleted the thread, cannot find it now.

The 2 states are (It's a tree DP, so for each vertex i, we consider only its subtrees and itself):

1. Maximum number of edges with the vertex not "full" (ie. connected to no more than 1 vertex, the vertex can still connect to the parent).
2. Maximum number of edges with the vertex "full" (ie. connected to 2 vertices already).