Blossom algorithm: Difference between revisions

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m Blossoms and contractions: Removed invisible unicode characters + other fixes, replaced: → (2) using AWB
Blossoms and contractions: Doesn't matter whether DFS or BFS - pseudocode later in the article specifies neither
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'''''Finding Blossoms:'''''
* Using DFS "Depth-First-Search", traverseTraverse 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 an odd-length cycle and hence 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''.