Bipartite graphs separate vertices sets from "summary" of Introduction to Graph Theory by Douglas Brent West
A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set. This property of bipartite graphs is fundamental to their structure and behavior. One key implication of this property is that bipartite graphs separate their vertices into distinct sets. Each set contains vertices that are only connected to vertices in the other set, and no edges exist between vertices within the same set. This separation is a defining characteristic of bipartite graphs and plays a crucial role in understanding their properties and applications. The separation of vertices sets in bipartite graphs has important implications for various graph-theoretic concepts and problems. For example, when considering the connectivity o...
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