20 years of Negami's planar cover conjecture

Investor logo

Warning

This publication doesn't include Faculty of Sports Studies. It includes Faculty of Informatics. Official publication website can be found on muni.cz.
Authors

HLINĚNÝ Petr

Year of publication 2008
MU Faculty or unit

Faculty of Informatics

Citation
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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info