Matched drawings of planar graphs

Authors:
Emilio Di Giacomo;Walter Didimo;Marc van Kreveld;Giuseppe Liotta;Bettina Speckmann
Affiliations:
Dip. di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia;Dip. di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia;Department of Computer Science, Utrecht University;Dip. di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia;Department of Mathematics and Computer Science, TU Eindhoven
Venue:
GD'07 Proceedings of the 15th international conference on Graph drawing
Year:
2007

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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.