Discussiones Mathematicae Graph Theory 31(2) (2011)
387-395

doi: 10.7151/dmgt.1553

Ingo Schiermeyer
Institut für Diskrete Mathematik und Algebra |

**Keywords:** rainbow colouring, rainbow connectivity, extremal problem

**2010 Mathematics Subject Classification:** 05C35, 05C15.

[1] | J.C. Bermond, On Hamiltonian Walks, Proc. of the Fifth British Combinatorial Conference, Aberdeen, 1975, Utlitas Math. XV (1976) 41--51. |

[2] | J.A. Bondy and U.S.R. Murty, Graph Theory (Springer, 2008), doi: 10.1007/978-1-84628-970-5. |

[3] | S. Chakraborty, E. Fischer, A. Matsliah and R. Yuster, Hardness and algorithms for rainbow connectivity, Proceedings STACS 2009, to appear in J. Combin. Optim. |

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

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

[6] | G.A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. 2 (1952) 69--81, doi: 10.1112/plms/s3-2.1.69. |

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

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

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

[10] | V.B. Le and Z. Tuza, Finding optimal rainbow connection is hard, preprint 2009. |

Received 5 January 2010

Revised 14 January 2011

Accepted 17 January 2011