Planar graphs are a type of graph that can be embedded in a plane in such a way that their edges do not cross each other. This property makes planar graphs particularly useful for a variety of applications in computer science, such as network design, routing algorithms, and graph visualization. Planar graphs have a number of interesting properties and characteristics, such as the fact that they do not contain any subgraphs that are isomorphic to the complete graph K5 or the complete bipartite graph K3,3. This property is known as Kuratowski's theorem, and it provides a useful characterization of planar graphs. Research on planar graphs often focuses on algorithms for finding planar embeddings, determining planarity, and analyzing the structural properties of planar graphs. This research has important implications for areas such as graph theory, computational geometry, and network science.