Augmenting paths are neat:
- An augmenting path has one more red edge than green. Why? Start
and end on red.
- Flipping the color of edges on the augmenting path results in a
valid matching. Why? Turning a green edge red could never hurt. The
new green edges all emanate from nodes with no green edges (or
formerly one green edge, now red).
- Therefore, after flipping the colors, our matching is bigger by
one edge.
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