International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 185346, 25 pages
Research Article

Two Sufficient Conditions for Hamilton and Dominating Cycles

Institute for Informatics and Automation Problems, National Academy of Sciences, Street P. Sevak 1, Yerevan 0014, Armenia

Received 24 March 2012; Accepted 14 August 2012

Academic Editor: Marianna Shubov

Copyright © 2012 Zh. G. Nikoghosyan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove that if is a 2-connect graph of size (the number of edges) and minimum degree with , where when and when , then each longest cycle in is a dominating cycle. The exact analog of this theorem for Hamilton cycles follows easily from two known results according to Dirac and Nash-Williams: each graph with is hamiltonian. Both results are sharp in all respects.