1. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm
Basic idea is:
Start with a forest of n vertices and no edges.
Add edges to the forest in non-decreasing order of weight.
Only add an edge if it joins together two different sub-trees.

2. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 5 3 2 f c

3. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 5 3 2 f c

4. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

5. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

6. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 ? b d e 2 4 5 3 2 f c

7. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 ? b d e 2 4 5 3 2 f c

8. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

9. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

10. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

11. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

12. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 5 3 ? 2 f c

13. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 5 3 ? 2 f c

14. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 ? 5 3 2 f c

15. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 ? 5 3 2 f c

16. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 ? b d e 2 4 5 3 2 f c

17. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 4 3 1 ? b d e 2 4 5 3 2 f c

18. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 ? 4 3 1 b d e 2 4 5 3 2 f c

19. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g 3 ? 4 3 1 b d e 2 4 5 3 2 f c

20. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

21. Minimum Spanning Trees (MSTs)
Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c