skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Sanka, Masahiro"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, The Electronic Journal of Combinatorics)
    Let $$G$$ be a $$t$$-tough graph on $$n\ge 3$$ vertices for some $t>0$. It was shown by Bauer et al. in 1995 that if the minimum degree of $$G$$ is greater than $$\frac{n}{t+1}-1$$, then $$G$$ is hamiltonian. In terms of Ore-type hamiltonicity conditions, the problem was only studied when $$t$$ is between 1 and 2, and recently the second author proved a general result. The result states that if the degree sum of any two nonadjacent vertices of $$G$$ is greater than $$\frac{2n}{t+1}+t-2$$, then $$G$$ is hamiltonian. It was conjectured in the same paper that the $+t$ in the bound $$\frac{2n}{t+1}+t-2$$ can be removed. Here we confirm the conjecture. The result generalizes the result by Bauer, Broersma, van den Heuvel, and Veldman. Furthermore, we characterize all $$t$$-tough graphs $$G$$ on $$n\ge 3$$ vertices for which $$\sigma_2(G) = \frac{2n}{t+1}-2$$ but $$G$$ is non-hamiltonian. 
    more » « less
    Full Text Available