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  • 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 %22if%22 direction is easy, and some supporting weaker statements have been shown by him, the conjecture is still open, after more than 20 years of intensive investigation. We review the (quite significant) progress made so far in solving Negami's conjecture, and propose possible promising directions of future research.
  • 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 %22if%22 direction is easy, and some supporting weaker statements have been shown by him, the conjecture is still open, after more than 20 years of intensive investigation. We review the (quite significant) progress made so far in solving Negami's conjecture, and propose possible promising directions of future research. (en)
Title
  • 20 years of Negami's planar cover conjecture
  • 20 years of Negami's planar cover conjecture (en)
skos:prefLabel
  • 20 years of Negami's planar cover conjecture
  • 20 years of Negami's planar cover conjecture (en)
skos:notation
  • RIV/00216224:14330/10:00049900!RIV12-GA0-14330___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/08/0308), Z(MSM0021622419)
http://linked.open...iv/cisloPeriodika
  • 4
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 300901
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14330/10:00049900
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • planar covers; projective embedding (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • JP - Japonsko
http://linked.open...ontrolniKodProRIV
  • [23BA51523D0A]
http://linked.open...i/riv/nazevZdroje
  • Graphs and Combinatorics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 26
http://linked.open...iv/tvurceVysledku
  • Hliněný, Petr
http://linked.open...ain/vavai/riv/wos
  • 000279129400007
http://linked.open...n/vavai/riv/zamer
issn
  • 0911-0119
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/s00373-010-0934-9
http://localhost/t...ganizacniJednotka
  • 14330
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