论文标题
在艰难图和极端示例中用于hamiltonity的矿石型条件
An Ore-type condition for hamiltonicity in tough graphs and the extremal examples
论文作者
论文摘要
令$ g $为$ n \ ge 3 $顶点上的$ t $ tough图，对于某些$ t> 0 $。 Bauer等人表明。在1995年，如果$ g $的最低度大于$ \ frac {n} {t+1} -1 $，则$ g $是哈密顿人。就矿石型汉密尔顿条件而言，只有在$ t $ 1到2介于2 $之间，就研究了问题，最近作者证明了一般结果。结果指出，如果$ g $的任何两个非附在顶点的度数大于$ \ frac {2n} {t+1}+t-2 $，则$ g $是汉密尔顿人。在同一篇论文中，它是可以删除的$ \ frac {2n} {2n} {2n} {t+1}+t-2 $的``$+t $'''可以删除的。在这里我们确认了猜想。结果概括了Bauer，Broersma，broersma，broersma，van den Heuvel和Veldman和Veldermore的结果。 $σ_2（g）= \ frac {2n} {t+1} -2 $，但$ g $是非hamiltonian。
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 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 $σ_2(G) = \frac{2n}{t+1}-2$ but $G$ is non-hamiltonian.
