Simultaneous Orthogonal PlanarityAngelini, Patrizio and Chaplick, Steven and Cornelsen, Sabine and Da Lozzo, Giordano and Di Battista, Giuseppe and Eades, Peter and Kindermann, Philipp and Kratochvíl, Jan and Lipp, Fabian and Rutter, Ignaz (2016) Simultaneous Orthogonal Planarity. In: Graph Drawing and Network Visualization. GD 2016, September, 19.  21., 2016 , pp. 532545(Official URL: http://dx.doi.org/10.1007/9783319501062_41). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319501062_41
AbstractWe introduce and study the ORTHOSEFEk 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 NPcomplete 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 polynomialtime 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.
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