Donovan Young on Nostr: A complete \(k\)-partite graph consists of \(k\) sets of vertices. There are no edges ...

A complete \(k\)-partite graph consists of \(k\) sets of vertices. There are no edges connecting vertices in the same set. Each vertex in the graph is connected to \( \it all \) the vertices outside its own set.

In a perfect matching a subset of edges are chosen such that each vertex of the original graph belongs to exactly one of the chosen edges.

In this thread I will ask some questions about the "typical" perfect matching for \(k\)-partite graphs with asymptotically large numbers of vertices.