On the Erd\H{o}s-P\'osa property for immersions and topological minors in tournaments

We consider the Erd\H{o}s-P\'osa property for immersions and topological minors in tournaments. prove that every simple digraph $H$, $k\in \mathbb{N}$, tournament $T$, following statements hold: (i) If $T$ one cannot find $k$ arc-disjoint immersion copies of then there exists a set $\mathcal{O}_H(k^3)$ arcs intersects all $H$ $T$. (ii) vertex-disjoint minor $\mathcal{O}_H(k\log k)$ vertices This improves results Raymond [DMTCS '18], who proved similar under assumption is strongly connected.