Discussiones Mathematicae Graph Theory 32(4) (2012)
705-724

doi: 10.7151/dmgt.1636

Garry Johns, Ryan Jones^{1},^{2}Kyle Kolasinski and Ping Zhang^{2}^{2}
Western Michigan University^{2} |

**Keywords:** powers of a strong oriented graph, distance-colored digraphs, Hamiltonian-colored digraphs, Hamiltonian coloring exponents

**2010 Mathematics Subject Classification:** 05C12, 05C15, 05C20, 05C45.

[1] | G. Chartrand, R. Jones, K. Kolasinski and P. Zhang, On the Hamiltonicity of distance-colored graphs, Congr. Numer. 202 (2010) 195--209. |

[2] | G. Chartrand, K. Kolasinski and P. Zhang, The colored bridges problem, Geographical Analysis 43 (2011) 370--382, doi: 10.1111/j.1538-4632.2011.00827.x. |

[3] | G. Chartrand, L. Lesniak and P. Zhang, Graphs & Digraphs, Fifth Edition (Chapman & Hall/CRC, Boca Raton, FL, 2011). |

[4] | H. Fleischner, The square of every nonseparable graph is Hamiltonian, Bull. Amer. Math. Soc. 77 (1971) 1052--1054, doi: 10.1090/S0002-9904-1971-12860-4. |

[5] | A. Ghouila-Houri, Une condition suffisante d'existence d'un circuit Hamiltonien, C. R. Acad. Sci. Paris 251 (1960) 495--497. |

[6] | R. Jones, K. Kolasinski and P. Zhang, On Hamiltonian-colored graphs, Util. Math. to appear. |

[7] | M. Sekanina, On an ordering of the set of vertices of a connected graph, Publ. Fac. Sci. Univ. Brno 412 (1960) 137--142. |

Received 7 July 2011

Revised 10 December 2011

Accepted 21 December 2011