Two Sufficient Conditions for Hamilton and Dominating Cycles - Zh. G. Nikoghosyan (International Journal of Mathematics and Mathematical Sciences)
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.