Some remarks on the Gromov width of homogeneous Hodge manifolds

We provide an upper bound for the Gromov width of compact homogeneous Hodge manifolds $(M, \omega)$ with $b_2(M)=1$. As an application we obtain an upper bound on the Seshadri constant $\epsilon (L)$ where $L$ is the ample line bundle on $M$ such that $c_1(L)=[\frac{\omega}{\pi}]$.