The Joint Crossing Number problem asks for a simultaneous embedding of two disjoint graphs into one surface such that the number of edge crossings (between the two graphs) is minimized. It was introduced by Negami in 2001 in connection with diagonal flips in triangulations of surfaces, and subsequently investigated in a general form for smallgenus surfaces. We prove that all of the commonly considered variants of this problem are NP-hard already in the orientable surface of genus 6, by a reduction from a special variant of the anchored crossing number problem of Cabello and Mohar.
CITATION STYLE
Hlinéný, P., & Salazar, G. (2015). On Hardness of the Joint Crossing Number. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9472 LNCS, pp. 603–613). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-662-48971-0_51
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