The crossing number of the generalized Petersen graph $P[3k,k]$

Fiorini, Stanley, and Gauci, John Baptist. "The crossing number of the generalized Petersen graph $P[3k,k]$." Mathematica Bohemica 128.4 (2003): 337-347. <http://eudml.org/doc/249227>.

@article{Fiorini2003,
abstract = {Guy and Harary (1967) have shown that, for $k\ge 3$, the graph $P[2k,k]$ is homeomorphic to the Möbius ladder $\{M_\{2k\}\}$, so that its crossing number is one; it is well known that $P[2k,2]$ is planar. Exoo, Harary and Kabell (1981) have shown hat the crossing number of $P[2k+1,2]$ is three, for $k\ge 2.$ Fiorini (1986) and Richter and Salazar (2002) have shown that $P[9,3]$ has crossing number two and that $P[3k,3]$ has crossing number $k$, provided $k\ge 4$. We extend this result by showing that $P[3k,k]$ also has crossing number $k$ for all $k\ge 4$.},
author = {Fiorini, Stanley, Gauci, John Baptist},
journal = {Mathematica Bohemica},
keywords = {graph; drawing; crossing number; generalized Petersen graph; Cartesian product; graph; drawing; crossing number; generalized Petersen graph; Cartesian product},
language = {eng},
number = {4},
pages = {337-347},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The crossing number of the generalized Petersen graph $P[3k,k]$},
url = {http://eudml.org/doc/249227},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Fiorini, Stanley
AU - Gauci, John Baptist
TI - The crossing number of the generalized Petersen graph $P[3k,k]$
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 4
SP - 337
EP - 347
AB - Guy and Harary (1967) have shown that, for $k\ge 3$, the graph $P[2k,k]$ is homeomorphic to the Möbius ladder ${M_{2k}}$, so that its crossing number is one; it is well known that $P[2k,2]$ is planar. Exoo, Harary and Kabell (1981) have shown hat the crossing number of $P[2k+1,2]$ is three, for $k\ge 2.$ Fiorini (1986) and Richter and Salazar (2002) have shown that $P[9,3]$ has crossing number two and that $P[3k,3]$ has crossing number $k$, provided $k\ge 4$. We extend this result by showing that $P[3k,k]$ also has crossing number $k$ for all $k\ge 4$.
LA - eng
KW - graph; drawing; crossing number; generalized Petersen graph; Cartesian product; graph; drawing; crossing number; generalized Petersen graph; Cartesian product
UR - http://eudml.org/doc/249227
ER -