spanning-tree

Given a undirected and connected graph G, find a spanning tree whose diameter is the minimum. singhsumit linked the relevant paper by Hassin and Tamir , entitled "On the minimum diameter spanning tree problem", but his answer is currently deleted. The main idea from the paper is that finding a minimum diameter spanning tree in an undirected graph can be accomplished by finding the "absolute 1-center" of the graph and returning a shortest path tree rooted there. The absolute 1-center is the point, either on a vertex or an edge, from which the distance to the furthest vertex is minimum. This can

I have a connected, undirected graph with edges that are each either black or white, and an integer k. I'm trying to write an algorithm that tells whether or not a spanning tree exists with exactly k black edges (doesn't necessarily have to find the actual tree). I used Kruskal's algorithm to find the minimum and maximum possible number of black edges in a spanning tree. If k is outside this range, no spanning tree with k edges can exist. But I'm having trouble wrapping my mind around whether there is necessarily a spanning tree for every k within that range. My intuition says yes, and it's