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===Analysis===
The forest ''F'' constructed by the ''find_augmenting_path()'' function is an alternating forest.<ref name = "kenyon report">{{cite
| author1 = Kenyon, Claire
| author2 = Lovász, László
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| contribution = Algorithmic Discrete Mathematics
| title = Technical Report CS-TR-251-90, Department of Computer Science, Princeton University
}}</ref>
* a tree ''T'' in ''G'' is an '''alternating tree''' with respect to ''M'', if
** ''T'' contains exactly one exposed vertex ''r'' called the tree root
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