@inproceedings{0d92b60762d342bc892c3a5455242ef9,

title = "Simultaneous Orthogonal Planarity",

abstract = "We introduce and study the OrthoSEFE-k problem: Given k planar graphs each with maximum degree 4 and the same vertex set, do they admit an OrthoSEFE, that is, is there an assignment of the vertices to grid points and of the edges to paths on the grid such that the same edges in distinct graphs are assigned the same path and such that the assignment induces a planar orthogonal drawing of each of the k graphs? We show that the problem is NP-complete for k >= 3 even if the shared graph is a Hamiltonian cycle and has sunflower intersection and for k >= 2 even if the shared graph consists of a cycle and of isolated vertices. Whereas the problem is polynomial-time solvable for k = 2 when the union graph has maximum degree five and the shared graph is biconnected. Further, when the shared graph is biconnected and has sunflower intersection, we show that every positive instance has an OrthoSEFE with at most three bends per edge.",

author = "Patrizio Angelini and Steven Chaplick and Sabine Cornelsen and Lozzo, {Giordano Da} and Battista, {Giuseppe Di} and Peter Eades and Philipp Kindermann and Jan Kratochv{\'i}l and Fabian Lipp and Ignaz Rutter",

note = "DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.",

year = "2016",

doi = "10.1007/978-3-319-50106-2_41",

language = "English",

series = "Lecture Notes in Computer Science",

publisher = "Springer Nature Switzerland AG",

pages = "532--545",

booktitle = "Graph Drawing and Network Visualization. GD 2016",

}