On the Relationship between Incidence Systems and Multipartite Graphs.

Abstract

This article presents the connection between incidence systems and multipartite graphs by using category theory. There is a fully faithful functor from the category of incidence systems to the category of multipartite graphs. Therefore, multipartite graphs are good models representing incidence systems, and vice versa. Due to this connection, some properties of incidence systems and geometries can be explained by graph theory, and in the same way, some properties of multipartite graphs can be explained by building theory.