Abstract:
Focusing on the Outerplanar graph family, we present relevant methodologies and known techniques for computing finite obstruction sets under a well-quasi-ordering. We generalise Outerplanarity to k-Apex-Outerplanar, and give a finite state congruence as well as a proven finite state membership algorithm for the k = 1 case, with a lower bound than was previously known. Later we describe our automated search for the Apex-Outerplanar graphs, where we find the full list of obstructions for the first time using this method.