Abstract
One of the earliest results about hamiltonian graphs was given by Dirac. He showed that if a graphG has orderp and minimum degree at least $$\frac{p}{2}$$ thenG is hamiltonian. Moon and Moser showed that a balanced bipartite graph (the two partite sets have the same order)G has orderp and minimum degree more than $$\frac{p}{4}$$ thenG is hamiltonian. In this paper, their idea is generalized tok-partite graphs and the following result is obtained: LetG be a balancedk-partite graph with orderp = kn. If the minimum degree $$\delta (G) > \left\{ {\begin{array}{*{20}c} {\left( {\frac{k}{2} - \frac{1}{{k + 1}}} \right)n if k is odd } \\ {\left( {\frac{k}{2} - \frac{2}{{k + 2}}} \right)n if k is even} \\ \end{array} } \right.$$ thenG is hamiltonian. The result is best possible.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.