Discussiones Mathematicae Graph Theory 33(3) (2013)
571-582

doi: 10.7151/dmgt.1684

Marián Klešč and Jana Petrillová
Faculty of Electrical Engineering and Informatics |

**Keywords:** graph, drawing, crossing number, Cartesian product, path, tree

**2010 Mathematics Subject Classification:** 05C10, 05C38.

[1] | L.W. Beineke and R.D. Ringeisen, On the crossing numbers of products of cycles and graphs of order four, J. Graph Theory 4 (1980) 145--155, doi: 10.1002/jgt.3190040203. |

[2] | D. Bokal, On the crossing number of Cartesian products with paths, J. Combin. Theory (B) 97 (2007) 381--384, doi: 10.1016/j.jctb.2006.06.003. |

[3] | S. Jendrol' and M. Ščerbová, On the crossing numbers of , Časopis Pro Pěstování Matematiky S and _{m} × P_{n}S_{m} × C_{n} 107 (1982) 225--230. |

[4] | M. Klešč, The crossing numbers of Cartesian products of stars and paths or cycles, Math. Slovaca 41 (1991) 113--120. |

[5] | M. Klešč, The crossing numbers of products of paths and stars with , J. Graph Theory 4-vertex graphs 18 (1994) 605--614. |

[6] | M. Klešč, The crossing number of , Tatra Mt. Math. Publ. K and _{2,3} × P_{n}K_{2,3} × S_{n} 9 (1996) 51--56. |

[7] | M. Klešč, The crossing numbers of products of , Discuss. Math. Graph Theory 4-vertex graphs with paths and cycles 19 (1999) 59--69, doi: 10.7151/dmgt.1085. |

[8] | M. Klešč, The crossing numbers of Cartesian products of paths with , Discrete Math. 5-vertex graphs 233 (2001) 353--359, doi: 10.1016/S0012-365X(00)00251-X. |

[9] | D. Kravecová, The crossing number of , Creat. Math. Inform. P^{2}_{5} × P_{n} 28 (2012) 49--56. |

[10] | Y.H. Peng and Y.C. Yiew, The crossing number of , Discrete Math. P(3,1) × P_{n} 306 (2006) 1941--1946, doi: 10.1016/j.disc.2006.03.058. |

[11] | J. Wang and Y. Huang, The crossing number of , Acta Math. Sci.,Ser. A, Chin. Ed. K_{2,4} × P_{n} 28 (2008) 251--255. |

[12] | L. Zhao, W. He, Y. Liu and X. Ren, The crossing number of two Cartesian products, Int. J. Math. Comb. 1 (2007) 120--127. |

[13] | W. Zheng, X. Lin, Y. Yang and Ch. Cui, On the crossing number of □K_{m} , Graphs Combin. P_{n} 23 (2007) 327--336, doi: 10.1007/s00373-007-0726-z. |

Received 30 November 2011

Revised 12 April 2012

Accepted 17 April 2012