Minimum Spanning Trees
Spanning trees and the minimum spanning tree; the cut property and the cycle property with their exact conditions; Kruskal with union-find, traced edge by edge on a six-vertex graph and drawn with the acceptance order; Prim with a priority queue on the same graph and its cost for array, binary-heap and Fibonacci-heap queues; when the MST is unique and a test for it; effects of adding, scaling or squaring weights with the solved GATE CS 2025 Set 2 Q.37; counting spanning trees; MST versus shortest-path tree.
