20 years of Negami's planar cover conjecture

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F10%3A00049900" target="_blank" >RIV/00216224:14330/10:00049900 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00373-010-0934-9" target="_blank" >http://dx.doi.org/10.1007/s00373-010-0934-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00373-010-0934-9" target="_blank" >10.1007/s00373-010-0934-9</a>

Result language
angličtina
Original language name
20 years of Negami's planar cover conjecture
Original language 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 "if" 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.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA201%2F08%2F0308" target="_blank" >GA201/08/0308: Utilization of structural and "Width" parameters in combinatorics and algorithmic complexity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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