Ores condition for hamiltonicity in tough graphs

Let $G$ be a $t$-tough graph on $nge 3$ 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 Ores conditions in this direction, the problem was only studied when $t$ is between 1 and 2. In this paper, we show 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.