On Hardness of the Joint Crossing Number

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9472)


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 small-genus 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Faculty of InformaticsMasaryk University BrnoBrnoCzech Republic
  2. 2.Instituto de FisicaUniversidad Autonoma de San Luis PotosiSan Luis PotosiMexico

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