Four-searchable biconnected outerplanar graphs

This paper deals with constructing obstruction sets for two subclasses of 4-searchable graphs. We first characterize the 4-searchable biconnected outerplanar graphs by listing all graphs that cannot be their minors; we then give a constructive characterization of such graphs. We also characterize the 4-searchable biconnected generalized wheel graphs by listing all graphs that cannot be their minors. Crown Copyright (C) 2021 Published by Elsevier B.V. All rights reserved.