MaxSTs
A maximum spanning tree (MaxST) of a weighted undirected graph G=(V,E) with edge weights w is a spanning tree T⊆E that maximizes the sum of its edge weights ∑_{e∈T} w(e). If G is connected, a MaxST exists and is a single tree; if G is disconnected, one forms a maximum spanning forest by taking a MaxST in each connected component.
MaxSTs are analogous to minimum spanning trees but aim to maximize total weight. If all edge weights
Computing a MaxST can be done with standard MST algorithms adapted for maximization. Kruskal’s algorithm can
Relation to minimum spanning trees: negating all edge weights converts a MaxST problem to a standard MinST
Applications of MaxSTs include network design scenarios where higher-weight edges reflect greater capacity, reliability, or bandwidth,