New Extensions of Dirac's Theorems - Mossine S. Koulakzian; Carlen M. Mosesyan; Zhora G. Nikoghosyan (Изд-во НАН РА)
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.
Keywords: Mathematics