Closely related concepts to complete subgraphs are [[subdivision (graph theory)|subdivision]]s of complete graphs and complete [[graph minor]]s. In particular, [[Kuratowski's theorem]] and [[Wagner's theorem]] characterize [[planar graph]]s by forbidden complete and [[complete bipartite graph|complete bipartite]] subdivisions and minors, respectively. | Closely related concepts to complete subgraphs are [[subdivision (graph theory)|subdivision]]s of complete graphs and complete [[graph minor]]s. In particular, [[Kuratowski's theorem]] and [[Wagner's theorem]] characterize [[planar graph]]s by forbidden complete and [[complete bipartite graph|complete bipartite]] subdivisions and minors, respectively. |