Bipartite theory and matching in Semigraphs

There are a variety of approaches to describe bipartite theory in graph theory. The solution of matching issues on bipartite graphs is frequently more straightforward than the solution on non-bipartite graphs. The Dulmage Mendelsohn decomposition, in particular, can be used to locate the best possible matches. The bipartite theory, matchings, and assignment problems in semigraphs are the focus of this paper.