About: 20 years of Negami's planar cover conjecture

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (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/00216224:14330/08:00044260!RIV11-MSM-14330___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0545), Z(MSM0021622419)
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Hliněný, Petr
http://linked.open.../riv/druhVysledku	O - Ostatní výsledky nezařaditelné do žádného z výše uvedených druhů výsledku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Fakulta informatiky
http://linked.open...dnocenehoVysledku	407588
http://linked.open...ai/riv/idVysledku	RIV/00216224:14330/08:00044260
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	planar covers; projective embedding (en)
http://linked.open.../riv/klicoveSlovo	planar covers projective embedding
http://linked.open...ontrolniKodProRIV	[0BB42D81CD67]
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science
http://linked.open...UplatneniVysledku	2008
http://linked.open...iv/tvurceVysledku	Hliněný, Petr
http://linked.open...n/vavai/riv/zamer	Highly Parallel and Distributed Computing Systems
http://localhost/t...ganizacniJednotka	14330

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