A minimum spanning forest of a weighted undirected graph is a spanning forest of minimum total edge weight. Equivalently, its restriction to each connected component is a minimum spanning tree of that component. For a connected graph, a minimum spanning forest is therefore a minimum spanning tree.
Minimum Spanning Forest
See also
Kruskal's Algorithm, Minimum Spanning TreeExplore with Wolfram|Alpha
References
Cormen, T. H.; Leiserson, C. E.; Rivest, R. L.; and Stein, C. Introduction to Algorithms, 2nd ed. Cambridge, MA: MIT Press, 2001.Cite this as:
Weisstein, Eric W. "Minimum Spanning Forest." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MinimumSpanningForest.html