Kruskal's algorithm scans edges from cheapest to most expensive. The key check is local and exact: accept an edge only when it does not create a cycle in the current forest.
highlighted = computed this step
Sorted edge scan
Kruskal accepts 5 edges and rejects 4. Motivation: scanning from cheap to expensive makes each decision local while the forest records what is already connected.
accepted=5rejected=4
First rejected edge
The first rejected edge has weight 4 and its existing path is B-C-D. Why: adding that edge would close a cycle, so the rejection is explained by an exact path witness.
B−D rejected by path B−C−D
Later cycle witnesses
The other reject witnesses are A-B-C, D-C-E, and E-C-D-F. Interpretation: every rejected edge is explained by the path already present in the forest, not by a visual guess.
reject means connected already
Diagram note
Certificate note: every accept or reject entry is recomputed from union-find and the current forest. Pixel positions are rounded for layout; every number shown is exact.