A Characteristic Approach to Bipartite Graphs and Incidence Graphs

A ‘bipartite characteristic’ parameter is defined for bipartite graphs that mimics the (Euler) characteristic—the number of vertices, minus the number of edges, plus the number of triangles, minus the number of 4-cliques, etc.—of general graphs. This allows the characterization of linear, totally balanced, acyclic, tree, and biacyclic hypergraphs in terms of the bipartite characteristic values of their incidence graphs.