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Abstract: 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 , , and . Further, it initiates the study of the matched drawability of triples of planar graphs: it presents an algorithm to 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. [Copyright &y& Elsevier]

Abstract: This paper studies the problem of drawing directed acyclic graphs in three dimensions in the straight-line grid model so that all directed edges are oriented in a common (upward) direction. We show that there exists a family of outerplanar directed acyclic graphs whose volume requirement is super-linear. We also prove that for the case of directed trees a linear-volume upper bound is achievable. [Copyright &y& Elsevier]