Editing Kruskal's algorithm (section)

===Spanning tree===
Let <math>G</math> be a connected, weighted graph and let <math>Y</math> be the subgraph of <math>G</math> produced by the algorithm. <math>Y</math> cannot have a cycle, as by definition an edge is not added if it results in a cycle. <math>Y</math> cannot be disconnected, since the first encountered edge that joins two components of <math>Y</math> would have been added by the algorithm. Thus, <math>Y</math> is a spanning tree of <math>G</math>.