Discussiones Mathematicae Graph Theory 31(4) (2011)
709-735

doi: 10.7151/dmgt.1575

Mais Alkhateeb
Faculty of Mathematics and Computer Science | Anja Kohl
Faculty of Mathematics and Computer Science |

**Keywords:** coloring, *b*-coloring, *b*-chromatic number, *b*-continuity

**2010 Mathematics Subject Classification:** 05C15, 05C78.

[1] | D. Barth, J. Cohen and T. Faik, On the , Discrete Appl. Math. b-continuity property of graphs 155 (2007) 1761--1768, doi: 10.1016/j.dam.2007.04.011. |

[2] | T. Faik and J.-F. Sacle, Some b-continuous classes of graphs, Technical Report N1350, LRI (Universite de Paris Sud, 2003). |

[3] | J.L. Gross and J. Yellen, Handbook of Graph Theory (CRC Press, 2004). |

[4] | C.T. Hoang and M. Kouider, On the , Discrete Appl. Math. b-dominating coloring of graphs 152 (2005) 176--186, doi: 10.1016/j.dam.2005.04.001. |

[5] | R.W. Irving and D.F. Manlove, The , Discrete Appl. Math. b-chromatic number of a graph 91 (1999) 127--141, doi: 10.1016/S0166-218X(98)00146-2. |

[6] | J. Kará, J. Kratochvil and M. Voigt, , Preprint No. M 14/04, Technical University Ilmenau, Faculty for Mathematics and Natural Sciences (2004).b-continuity |

[7] | A. Kohl and I. Schiermeyer, Some Results on Reed's Conjecture about , Discrete Math. ω, Δ, and χ with respect to α 310 (2010) 1429--1438, doi: 10.1016/j.disc.2009.05.025. |

[8] | M. Kouider and M. Maheo, Some bounds for the , Discrete Math. b-chromatic number of a graph 256 (2002) 267--277, doi: 10.1016/S0012-365X(01)00469-1. |

[9] | M. Kouider and M. Zaker, Bounds for the , Discrete Math. b-chromatic number of some families of graphs 306 (2006) 617--623, doi: 10.1016/j.disc.2006.01.012. |

[10] | L. Rabern, A note on Reed's conjecture, SIAM J. Discrete Math. 22 (2008) 820--827, doi: 10.1137/060659193
. |

[11] | S. Radziszowski, Small Ramsey Numbers, Electronic Journal of Combinatorics, Dynamic Survey DS1 (2006). |

Received 15 April 2010

Revised 9 November 2010

Accepted 11 November 2010