20 years of Negami's planar cover conjecture
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | Graphs and Combinatorics |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/s00373-010-0934-9 |
| Field | General mathematics |
| Keywords | planar covers; projective embedding |
| 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. |
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