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@article{946888, author = {Hliněný, Petr}, article_location = {Tokyo}, article_number = {4}, doi = {http://dx.doi.org/10.1007/s00373-010-0934-9}, keywords = {planar covers; projective embedding}, language = {eng}, issn = {0911-0119}, journal = {Graphs and Combinatorics}, title = {20 years of Negami's planar cover conjecture}, volume = {26}, year = {2010} }
TY - JOUR ID - 946888 AU - Hliněný, Petr PY - 2010 TI - 20 years of Negami's planar cover conjecture JF - Graphs and Combinatorics VL - 26 IS - 4 SP - 525-536 EP - 525-536 PB - Springer Japan SN - 09110119 KW - planar covers KW - projective embedding N2 - 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. ER -
HLINĚNÝ, Petr. 20 years of Negami's planar cover conjecture. \textit{Graphs and Combinatorics}. Tokyo: Springer Japan, 2010, roč.~26, č.~4, s.~525-536. ISSN~0911-0119. Dostupné z: https://dx.doi.org/10.1007/s00373-010-0934-9.
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