A characterization of ?-outerplanar graphs
Lawrence Wargo · Journal of Graph Theory · 1996
Chartrand and Harary have shown that if G is a non-outerplanar graph such that, for every edge e, both the deletion G\e and the contraction G/e of e from G are outerplanar, then G is isomorphic to K4 or K2,3. An α-outerplanar graph is a graph which is not outerplanar such that, for some edge α, both G\α and G/α are outerplanar. We describe various results for the class of α-outerplanar graphs and obtain a characterization of the class. © 1996 John Wiley & Sons, Inc.