НАН РА. Математические вопросы кибернетики и вычислительной техники=Mathematical problems of computer science

New Extensions of Dirac's Theorems

Koulakzian, Mossine S. and Mosesyan, Carlen M. and Nikoghosyan, Zhora G. (2017) New Extensions of Dirac's Theorems. Математические вопросы кибернетики и вычислительной техники, № 48. pp. 14-18. ISSN 0131-4645

[img] PDF
Download (269Kb)

    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.

    Item Type: Article
    Additional Information: Դիրակի թեորեմների նոր ընդհանրացումներ / Մ. Քուլաքզյան, Կ. Մոսեսյան, Ժ. Նիկողոսյան: Новые обобщения теорем Дирака / М. Кулакзян, К. Мосесян, Ж. Никогосян
    Uncontrolled Keywords: Hamilton cycle, Longest cycle, Circumference, Minimum degree, Degree sequence.
    Subjects: Q Science > QA Mathematics
    Divisions: UNSPECIFIED
    Depositing User: FSL Bibl. Dept.
    Date Deposited: 10 Oct 2018 13:36
    Last Modified: 10 Oct 2018 13:36
    URI: http://compsci.asj-oa.am/id/eprint/878

    Actions (login required)

    View Item