In recent years there has been an increased interest in frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it becomes intractable for arbitrary graph databases. Existing approaches have therefore resorted to various heuristic strategies and restrictions of the search space, but have not identified a practically relevant tractable graph class beyond trees. In this paper, we define the class of so called tenuous outerplanar graphs, a strict generalization of trees, develop a frequent subgraph mining algorithm for tenuous outerplanar graphs that works in incremental polynomial time, and evaluate the algorithm empirically on the NCI molecular graph dataset
