The maximum matching of a bipartite graph is the matroid crossing of a partitioned matroid pair

from matroid The maximum matching of a bipartite graph is the matroid crossing of a partitioned matroid pair

• Focusing on the V1 side vertex, only one edge at most comes out of one vertex.
  • That is, split matroid.
• Same for V2 side
• The edge set that is matching is a common subset of these two
  • In other words matroid crossing.

https://app.mathsoc.jp/meeting_data/tokyo18mar/pdf/msjmeeting-2018mar-00f004.pdf - matroid crossing - incremental algorithm - The Maximum matching problem on 2-part graph is a split matroid pair crossing problem

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