Abstract
A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique y-coordinate. In this paper we introduce the concept of such matched drawings, which are a relaxation of simultaneous geometric embeddings with mapping. We study which classes of graphs allow matched drawings and show that (i) two 3-connected planar graphs or a 3-connected planar graph and a tree may not be matched drawable, while (ii) two trees or a planar graph and a planar graph of some special families—such as unlabeled level planar (ULP) graphs or the family of “carousel graphs”—are always matched drawable.
Research partially supported by the MIUR Project “MAINSTREAM: Algorithms for massive information structures and data streams”.
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Di Giacomo, E., Didimo, W., van Kreveld, M., Liotta, G., Speckmann, B. (2008). Matched Drawings of Planar Graphs. In: Hong, SH., Nishizeki, T., Quan, W. (eds) Graph Drawing. GD 2007. Lecture Notes in Computer Science, vol 4875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77537-9_19
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DOI: https://doi.org/10.1007/978-3-540-77537-9_19
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