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Քուլաքզյան Մ., Մոսեսյան Կ., Նիկողոսյան Ժ., Кулакзян М., Мосесян К., Никогосян Ж.
Title:
New Extensions of Dirac's Theorems
Other title:
Դիրակի թեորեմների նոր ընդհանրացումներ; Новые обобщения теорем Дирака
Creator:
Mossine S. Koulakzian ; Carlen M. Mosesyan ; Zhora G. Nikoghosyan
Subject:
Uncontrolled Keywords:
Hamilton cycle ; Longest cycle ; Circumference ; Minimum degree ; Degree sequence.
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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.