Matched Drawability of Graph Pairs and of Graph Triples

The contribution of this paper is twofold. It presents a new approach to the matched drawability problem of pairs of planar graphs and it provides four algorithms based on this approach for drawing the pairs <outerplane,maximal outerpillar>, <outerplane, generalized outerpath>, <outerplane, wheel> and <wheel, wheel>. Further, it initiates the study of thematched drawability of triples of planar graphs: it presents an algorithmto compute a matched drawing of a triple of cycles and an algorithm to compute a matched drawing of a caterpillar and two unlabeled level planar graphs. The results extend previous work on the subject and relate to existing literature about simultaneous embeddability and unlabeled level planarity.