Discussiones Mathematicae Graph Theory 32(4) (2012)
705-724
doi: 10.7151/dmgt.1636
Garry Johns1, Ryan Jones2, Kyle Kolasinski2 and Ping Zhang2
1 Saginaw Valley State University |
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