@article{8767610,
  abstract     = {{The dual of a polyhedron is a polyhedron -- or in graph theoretical terms: the dual of a 3-connected plane graph is a 3-connected plane graph. Astonishingly, except for sufficiently large facewidth, not much is known about the connectivity of the dual on higher surfaces. Are the duals of 3-connected embedded graphs of higher genus 3-connected, too? If not, which connectivity guarantees 3-connectedness of the dual? In this article, we give answers to some of these and related questions. We prove that there is no connectivity that guarantees the 3-connectedness or 2-connectedness of the dual for every genus, and give upper bounds for the minimum genus for which (with c > 2) a c-connected embedded graph with a dual that has a 1- or 2-cut can occur. We prove that already on the torus, we need 6-connectedness to guarantee 3-connectedness of the dual and 4-connectedness to guarantee 2-connectedness of the dual. In the last section, we answer a related question by Plummer and Zha on orientable embeddings of highly connected non-complete graphs.}},
  author       = {{Bokal, Drago and Brinkmann, Gunnar and Zamfirescu, Carol}},
  issn         = {{0364-9024}},
  journal      = {{JOURNAL OF GRAPH THEORY}},
  keywords     = {{Geometry and Topology,Discrete Mathematics and Combinatorics,connectivity,dual graph,embedded graph}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{182--209}},
  title        = {{The connectivity of the dual}},
  url          = {{http://doi.org/10.1002/jgt.22819}},
  volume       = {{101}},
  year         = {{2022}},
}

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