Discussiones Mathematicae Graph Theory 33(1) (2013)
181-192

doi: 10.7151/dmgt.1640

*Dedicated to Mietek Borowiecki on the occasion of his seventieth birthday*

Arnfried Kemnitz
Computational Mathematics, Technische Universität Braunschweig |
Jakub Przybyło and Mariusz Wożniak
AGH University of Science and Technology | Ingo Schiermeyer
Institut für Diskrete Mathematik und Algebra |

**Keywords:** rainbow-connected graph, rainbow colouring, rainbow connection number

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

[1] | J.A. Bondy and U.S.R. Murty, Graph Theory (Springer, 2008). |

[2] | Y. Caro, A. Lev, Y. Roditty, Z. Tuza, and R. Yuster, On rainbow connection, Electron. J. Combin. 15 (2008) #57. |

[3] | S. Chakraborty, E. Fischer, A. Matsliah, and R. Yuster, Hardness and algorithms for rainbow connectivity, J. Comb. Optim. 21 (2011) 330--347, doi: 10.1007/s10878-009-9250-9. |

[4] | L.S. Chandran, A. Das, D. Rajendraprasad, and N.M. Varma, Rainbow connection number and connected dominating sets, J. Graph Theory 71 (2012) 206--218, doi: 10.1002/jgt.20643. |

[5] | G. Chartrand, G.L. Johns, K.A. McKeon, and P. Zhang, Rainbow connection in graphs, Math. Bohemica 133 (2008) 85--98. |

[6] | A.B. Ericksen, A matter of security, Graduating Engineer & Computer Careers (2007) 24--28. |

[7] | J. Ekstein, P. Holub, T. Kaiser, M. Koch, S. Matos Camacho, Z. Ryjáček and I. Schiermeyer, The rainbow connection number in , Discrete Math, doi: 10.1016/j.disc.2012.04.022.2-connected graphs |

[8] | E. Györi, On division of graphs to connected subgraphs, Combinatorics, Vol. I, pp. 485--494, Colloq. Math. Soc. János Bolyai, 18, North-Holland, Amsterdam, 1978. |

[9] | A. Kemnitz and I. Schiermeyer, Graphs with rainbow connection number two, Discuss. Math. Graph Theory 31 (2011) 313--320, doi: 10.7151/dmgt.1547. |

[10] | M. Krivelevich and R. Yuster, The rainbow connection of a graph is , J. Graph Theory (at most) reciprocal to its minimum degree 63 (2010) 185--191. |

[11] | V.B. Le and Zs. Tuza, Finding optimal rainbow connection is hard, Preprint 2009. |

[12] | X. Li, M. Liu, and I. Schiermeyer, Rainbow connection number of dense graphs, to appear in Discuss. Math. Graph Theory.arXiv: 1110.5772v1 [math.CO] 2011. |

[13] | X. Li and Y. Sun, Rainbow Connections of Graphs, Springer Briefs in Math., Springer, New York, 2012. |

[14] | L. Lovász, A homology theory for spanning trees of a graph, Acta Math. Hungar. 30 (1977) 241--251, doi: 10.1007/BF01896190. |

[15] | I. Schiermeyer, Rainbow connection in graphs with minimum degree three, Lecture Notes Computer Science 5874 (2009) 432--437, doi: 10.1007/978-3-642-10217-2_42. |

Received 11 April 2012

Revised 11 July 2012

Accepted 11 July 2012