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DOI: 10.7155/jgaa.00507
Simultaneous Embeddings with Few Bends and Crossings
Vol. 23, no. 4, pp. 683713, 2019. Regular paper.
Abstract A simultaneous embedding with fixed edges ($\rm{S{\small EFE}}$) of two planar graphs $R$ and $B$ is a pair of plane drawings of $R$ and $B$ that coincide when restricted to the common vertices and edges of $R$ and $B$. We show that whenever $R$ and $B$ admit a $\rm{S{\small EFE}}$, they also admit a $\rm{S{\small EFE}}$ in which every edge is a polygonal curve with few bends and every pair of edges has few crossings. Specifically:

Submitted: December 2018.
Reviewed: April 2019.
Revised: May 2019.
Reviewed: July 2019.
Revised: July 2019.
Accepted: July 2019.
Final: August 2019.
Published: September 2019.
Communicated by
Stephen G. Kobourov
