Editing Outerplanar graph (section)

==History==
Outerplanar graphs were first studied and named by {{harvtxt|Chartrand|Harary|1967}}, in connection with the problem of determining the planarity of graphs formed by using a [[perfect matching]] to connect two copies of a base graph (for instance, many of the [[generalized Petersen graph]]s are formed in this way from two copies of a [[cycle graph]]). As they showed, when the base graph is [[biconnected graph|biconnected]], a graph constructed in this way is planar if and only if its base graph is outerplanar and the matching forms a [[dihedral group|dihedral]] permutation of its outer cycle. Chartrand and Harary also proved an analogue of [[Kuratowski's theorem]] for outerplanar graphs, that a graph is outerplanar if and only if it does not contain a [[Homeomorphism (graph theory)|subdivision]] of one of the two graphs ''K''<sub>4</sub> or ''K''<sub>2,3</sub>.