@inproceedings{a231c96b98514ff68877a3fd9398a90a,
title = "Matched drawings of planar graphs",
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{"}.",
author = "\{Di Giacomo\}, E. and W. Didimo and \{Kreveld, van\}, M.J. and G. Liotta and B. Speckmann",
year = "2008",
doi = "10.1007/978-3-540-77537-9\_19",
language = "English",
isbn = "978-3-540-77536-2",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "183--194",
editor = "S.K. Hong and T. Nishizeki and W. Quan",
booktitle = "Graph Drawing (15th International Symposium, GD'07, Sydney, Australia, September 23-26, 2007, Revised Papers)",
address = "Germany",
}