File:Prim's algorithm proof.svg

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DescriptionPrim's algorithm proof.svg	English: Diagram to assist in proof of Prim's algorithm. If $Y_{1}$ is a minimum spanning tree, and Y is the tree found by Prim's algorithm, we find e, the first edge added by the algorithm which is in $Y_{1}$ but not in Y. Let V be the vertices added to the tree up to that point. Then we find a path in $Y_{1}$ between the endpoints of e and find an edge f in that path with one endpoint in V. Then $Y_{1}-f+e$ is also a minimum spanning tree, and is in this case equal to Y. In general, more steps may be needed.
Date	14 November 2013
Source	Own work
Author	User:Dcoetzee

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	09:03, 15 November 2013		405 × 827 (31 KB)	wikimediacommons>Dcoetzee	{{Information \|Description ={{en\|1=Diagram to assist in proof of Prim's algorithm. If <math>Y_1</math> is a minimum spanning tree, and Y is the tree found by Prim's algorithm, we find ''e'', the first edge added by the algorithm which is in <math>Y_...

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