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In max-flow problems, like in matching problems, augmenting paths are paths where the amount of flow between the source and sink can be increased.

The majority of realistic matching problems are much more complex than those presented above.

An alternating path usually starts with an unmatched vertex and terminates once it cannot append another edge to the tail of the path while maintaining the alternating sequence.

Augmenting paths in matching problems are closely related to augmenting paths in maximum flow problems, such as the max-flow min-cut algorithm, as both signal sub-optimality and space for further refinement.

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