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20 Years of Negami’s Planar Cover Conjecture

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Abstract

In 1988, Seiya Negami published a conjecture stating that a graph G has a finite planar cover (i.e. a homomorphism from some planar graph onto G which maps the vertex neighbourhoods bijectively) if and only if G embeds in the projective plane. Though the “if” direction is easy, and over ten related research papers have been published during the past 20 years of investigation, this beautiful conjecture is still open in 2008. We give a short accessible survey on Negami’s conjecture and all the (so far) published partial results, and outline some further ideas to stimulate future research towards solving the conjecture.

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Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Botanická 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

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  1. Petr Hliněný
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Correspondence to Petr Hliněný.

Additional information

Supported by the Czech research grant GAČR 201/08/0308 and by the Institute for Theoretical Computer Science, project 1M0545.

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Hliněný, P. 20 Years of Negami’s Planar Cover Conjecture. Graphs and Combinatorics 26, 525–536 (2010). https://doi.org/10.1007/s00373-010-0934-9

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  • DOI: https://doi.org/10.1007/s00373-010-0934-9

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