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Statements

Subject Item
n2:RIV%2F00216224%3A14330%2F10%3A00049900%21RIV12-GA0-14330___
rdf:type
n17:Vysledek skos:Concept
dcterms:description
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.
dcterms:title
20 years of Negami's planar cover conjecture 20 years of Negami's planar cover conjecture
skos:prefLabel
20 years of Negami's planar cover conjecture 20 years of Negami's planar cover conjecture
skos:notation
RIV/00216224:14330/10:00049900!RIV12-GA0-14330___
n3:aktivita
n4:Z n4:P
n3:aktivity
P(GA201/08/0308), Z(MSM0021622419)
n3:cisloPeriodika
4
n3:dodaniDat
n6:2012
n3:domaciTvurceVysledku
n8:7595646
n3:druhVysledku
n11:J
n3:duvernostUdaju
n20:S
n3:entitaPredkladatele
n9:predkladatel
n3:idSjednocenehoVysledku
300901
n3:idVysledku
RIV/00216224:14330/10:00049900
n3:jazykVysledku
n16:eng
n3:klicovaSlova
planar covers; projective embedding
n3:klicoveSlovo
n19:planar%20covers n19:projective%20embedding
n3:kodStatuVydavatele
JP - Japonsko
n3:kontrolniKodProRIV
[23BA51523D0A]
n3:nazevZdroje
Graphs and Combinatorics
n3:obor
n18:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n15:GA201%2F08%2F0308
n3:rokUplatneniVysledku
n6:2010
n3:svazekPeriodika
26
n3:tvurceVysledku
Hliněný, Petr
n3:wos
000279129400007
n3:zamer
n7:MSM0021622419
s:issn
0911-0119
s:numberOfPages
12
n14:doi
10.1007/s00373-010-0934-9
n10:organizacniJednotka
14330