Blossom algorithm: Difference between revisions

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m Added how Blossoms are found in graphs.
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m Blossoms and contractions: Removed invisible unicode characters + other fixes, replaced: → (2) using AWB
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* Using DFS "Depth-First-Search", traverse the graph starting from an exposed or a free vertex.
* Starting from that vertex, label it as an outer vertex "'''''o'''"''.
* Alternate the labeling between vertices being inner "'''''i'''"''   and outer "'''''o'''"'' such that no two adjacent vertices have the same label.
* If we end up with two adjacent vertices labeled as outer "'''''o'''"''   then we have a blossom.
 
Define the '''contracted graph''' ''G’'' as the graph obtained from ''G'' by [[edge contraction|contracting]] every edge of ''B'', and define the '''contracted matching''' ''M’'' as the matching of ''G’'' corresponding to ''M''.