Other formats:
BibTeX
LaTeX
RIS
@article{575304,
author = {Hliněný, Petr and Thomas, Robin},
article_location = {New York},
article_number = {3},
keywords = {graph; planar cover; projective plane; minor},
language = {eng},
issn = {0364-9024},
journal = {Journal of Graph Theory},
title = {On possible counterexamples to Negami's planar cover conjecture},
url = {http://www3.interscience.wiley.com/cgi-bin/fulltext/108061224/ABSTRACT},
volume = {46},
year = {2004}
}
TY - JOUR
ID - 575304
AU - Hliněný, Petr - Thomas, Robin
PY - 2004
TI - On possible counterexamples to Negami's planar cover conjecture
JF - Journal of Graph Theory
VL - 46
IS - 3
SP - 183-206
EP - 183-206
PB - John Wiley & Sons
SN - 03649024
KW - graph
KW - planar cover
KW - projective plane
KW - minor
UR - http://www3.interscience.wiley.com/cgi-bin/fulltext/108061224/ABSTRACT
N2 - A simple graph $\H$ is a cover of a graph $\G$ if there exists a mapping $\varphi$ from $\H$ onto $\G$ such that $\varphi$ maps the neighbors of every vertex $v$ in $\H$ bijectively to the neighbors of $\varphi(v)$ in $\G$. Negami conjectured in 1986 that a connected graph has a finite planar cover if and only if it embeds in the projective plane. The conjecture is still open. It follows from the results of Archdeacon, Fellows, Negami, and the first author that the conjecture holds as long as the graph $\K_{1,2,2,2}$ has no finite planar cover. However, those results seem to say little about counterexamples if the conjecture was not true. We show that there are, up to obvious constructions, at most $16$ possible counterexamples to Negami's conjecture. Moreover, we exhibit a finite list of sets of graphs such that the set of excluded minors for the property of having finite planar cover is one of the sets in our list.
ER -
HLINĚNÝ, Petr and Robin THOMAS. On possible counterexamples to Negami's planar cover conjecture. \textit{Journal of Graph Theory}. New York: John Wiley \&{} Sons, 2004, vol.~46, No~3, p.~183-206. ISSN~0364-9024.
|
