Journal of Graph Algorithms and Applications
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Special Issue on Selected Papers from the Fifteenth International Symposium on Graph Drawing, GD 2007
Matched Drawings of Planar Graphs
Vol. 13, no. 3, pp. 423-445, 2009. Regular paper.
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 is 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 sufficiently restricted planar graph-such as an unlabeled level planar (ULP) graph or a graph of the family of "carousel graphs"-are always matched drawable.
Submitted: December 2007.
Reviewed: May 2008.
Revised: August 2008.
Accepted: November 2008.
Final: November 2008.
Published: November 2009.