Discussiones Mathematicae Graph Theory 32(4) (2012)
795-806

doi: 10.7151/dmgt.1642

Wayne Goddard and Honghai Xu
Dept of Mathematical Sciences |

**Keywords:** graph, coloring, packing, broadcast chromatic number

**2010 Mathematics Subject Classification:** 05C15, 05C69.

[1] | B. Brešar and S. Klavžar and D.F. Rall, On the packing chromatic number of Cartesian products, hexagonal lattice, and trees, Discrete Appl. Math. 155 (2007) 2303--2311, doi: 10.1016/j.dam.2007.06.008. |

[2] | J. Ekstein, J.Fiala, P.Holub and B. Lidický, The packing chromatic number of the square lattice is at least , preprint.12 |

[3] | J. Fiala and P.A. Golovach, Complexity of the packing coloring problem for trees, Discrete Appl. Math. 158 (2010) 771--778, doi: 10.1016/j.dam.2008.09.001. |

[4] | J. Fiala, S. Klavžar and B. Lidický, The packing chromatic number of infinite product graphs, European J. Combin. 30 (2009) 1101--1113, doi: 10.1016/j.ejc.2008.09.014. |

[5] | M.R. Garey and D.S. Johnson, Computers and Intractability, A guide to the Theory of NP-completeness (W. H. Freeman and Co., San Francisco, Calif., 1979). |

[6] | W. Goddard, S.M. Hedetniemi, S.T. Hedetniemi, J.M. Harris and D.F. Rall, Broadcast chromatic numbers of graphs, Ars Combin. 8 (2008) 33--49. |

[7] | C. Sloper, An eccentric coloring of trees, Australas. J. Combin. 29 (2004) 309--321. |

[8] | R. Soukal and P. Holub, A note on packing chromatic number of the square lattice, Electron. J. Combin. 17 (2010) Note 17, 7. |

[9] | D.B. West, Introduction to Graph Theory (Prentice Hall, NJ, USA, 2001). |

Received 27 August 2011

Revised 22 February 2012

Accepted 23 February 2012