@inbook{4fbb4391f2444cfc84d39da8491a6e05,

title = "On simultaneous planar graph embeddings",

abstract = "We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. In particular, given a mapping, we show how to embed two paths on an n x n grid, and two caterpillar graphs on a 3n x 3n grid. We show that it is not always possible to simultaneously embed three paths. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n) x O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n2) x O(n2) grid.",

author = "P. Brass and E. Cenek and Duncan, {Christian A.} and A. Efrat and C. Erten and D. Ismailescu and Kobourov, {S. G.} and A. Lubiw and Mitchell, {J. S.B.}",

note = "Funding Information: ✩ An extended abstract of this paper appeared in WADS 2003. * Corresponding author. E-mail addresses: peter@cs.ccny.cuny.edu (P. Brass), ewcenek@uwaterloo.edu (E. Cenek), duncan@cs.miami.edu (C.A. Duncan), alon@cs.arizona.edu (A. Efrat), cesim@cs.arizona.edu (C. Erten), dan.p.ismailescu@hofstra.edu (D.P. Ismailescu), kobourov@cs.arizona.edu (S.G. Kobourov), alubiw@uwaterloo.edu (A. Lubiw), jsbm@ams.sunysb.edu (J.S.B. Mitchell). 1 Partially supported by NSF Grant ACR-0222920. 2 Partially supported by Metron Aviation, Inc., NASA Ames Research (NAG2-1620), and the National Science Foundation (CCF-0431030, CCF-0528209).",

year = "2003",

doi = "10.1007/978-3-540-45078-8_22",

language = "English (US)",

isbn = "3540405453",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "243--255",

editor = "Frank Dehne and Jorg-Rudiger Sack and Michiel Smid",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}