from <a href="/en/matroid">matroid</a>
The maximum matching of a bipartite graph is the matroid crossing of a partitioned matroid pair
<img src="https://gyazo.com/a370998bd984fe19e25da836e8ab653f/thumb/1000" alt="image">
<ul>
<li>Focusing on the V1 side vertex, only one edge at most comes out of one vertex.<ul>
<li>That is, <a href="/en/split%20matroid">split matroid</a>.</li>
</ul>
</li>
<li>Same for V2 side</li>
<li>The edge set that is matching is a common subset of these two<ul>
<li>In other words <a href="/en/matroid%20crossing">matroid crossing</a>.</li>
</ul>
</li>
</ul>
<a href="https://app.mathsoc.jp/meeting_data/tokyo18mar/pdf/msjmeeting-2018mar-00f004.pdf">https://app.mathsoc.jp/meeting_data/tokyo18mar/pdf/msjmeeting-2018mar-00f004.pdf</a>
 - <a href="/en/matroid%20crossing">matroid crossing</a>
 - <a href="/en/incremental%20algorithm">incremental algorithm</a>
 - The <a href="/en/Maximum%20matching">Maximum matching</a> problem on <a href="/en/2-part%20graph">2-part graph</a> is a <a href="/en/split%20matroid">split matroid</a> pair crossing problem
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