(rev. 2020/02/26)
Kruskal Algorithm Theorem
Theorem 6.3.2: Kruskal's algorithm finds a minimal cost spanning tree. (In other words, it works.)
Definition 5: A set of edges is promising if it can be extended to form the edge set of a minimal cost spanning tree.
Definition 6: Suppose that B is a subset of the node set N of an undirected graph G=<N,E>. Suppose further that B is not all of N, and that B is not empty. An edge e={x,y} ∈ E is said to leave B if one of the ends (x or y) is in B and the other end is not in B. (Note: an edge e leaves B if and only if e provides a "bridge" from B to the complement of B.)
