Another go at perfect matchings but this time, we want to look at bipartite graphs. The difference is we don’t want to use Tutte’s theorem to help us. So what can we do?
We may proceed using an idea similar to the Tutte matrix. However, since the graph is bipartite, the Tutte matrix will have many zeroes. Therefore, we may simplify out representation of the adjacency matrix.
At the end we saw a neat application of using the inverse of our simplified matrix to tell us about the matchings in the graph.
I’m uploading the pictures of the chalk boards, but as a special treat, we get to look at Prof. Blum’s personal notes. If these are helpful please let me or the professor know.