@misc{Mossine_S._Koulakzian_New, author={Mossine S. Koulakzian and Carlen M. Mosesyan and Zhora G. Nikoghosyan}, howpublished={online}, publisher={Изд-во НАН РА}, abstract={Let G be a graph on n vertices with degree sequence ᶑ = d1 ≤ d2 ≤ ::: ≤ dn and let c be the circumference - the length of a longest cycle in G. In 1952, Dirac proved: (i) every graph with d1 ¸≥ n 2 is hamiltonian; (ii) in every 2-connected graph, c ≥ min \{n,2d1\}. In this paper we present the following two Dirac-type extensions: (iii) every graph with d± ≥ n 2 is hamiltonian; (iv) in every 2-connected graph, c ≥ min \{n,2dg\} The results are sharp.}, type={Հոդված}, title={New Extensions of Dirac's Theorems}, keywords={Mathematics}, }