Editing Outerplanar graph (section)

===Forbidden graphs===
Outerplanar graphs have a [[forbidden graph characterization]] analogous to [[Kuratowski's theorem]] and [[Wagner's theorem]] for planar graphs: a graph is outerplanar if and only if it does not contain a [[Homeomorphism (graph theory)|subdivision]] of the [[complete graph]] ''K''<sub>4</sub> or the [[complete bipartite graph]] ''K''<sub>2,3</sub>.<ref>{{harvtxt|Chartrand|Harary|1967}}; {{harvtxt|Sysło|1979}}; {{harvtxt|Brandstädt|Le|Spinrad|1999}}, Proposition 7.3.1, p. 117; {{harvtxt|Felsner|2004}}.</ref> Alternatively, a graph is outerplanar if and only if it does not contain ''K''<sub>4</sub> or ''K''<sub>2,3</sub> as a [[minor (graph theory)|minor]], a graph obtained from it by deleting and contracting edges.<ref>{{harvtxt|Diestel|2000}}.</ref>

A [[triangle-free graph]] is outerplanar if and only if it does not contain a subdivision of ''K''<sub>2,3</sub>.<ref name="s79"/>