A graph is 1-planar, if it admits a 1-planar embedding, where each edge has at most one crossing. Unfortunately, testing 1-planarity of a graph is known as NP-complete. This paper considers the problem of testing 2-planarity of a graph, in particular,testing full outer-2planarity of a graph. A graph is fully-outer-2-planar, if it admits a fully-outer-2-planar embedding such that every vertex is...