  It is well-known that every tournament contains a Hamilton path, and every
strongly connected tournament contains a Hamilton cycle. This paper establishes
transversal generalizations of these classical results. For a collection
$\mathbf{T}=\{T_1,\dots,T_m\}$ of not-necessarily distinct tournaments on a
common vertex set $V$, an $m$-edge directed graph $\mathcal{D}$ with vertices
in $V$ is called a $\mathbf{T}$-transversal if there exists a bijection
$\phi\colon E(\mathcal{D})\to [m]$ such that $e\in E(T_{\phi(e)})$ for all
$e\in E(\mathcal{D})$. We prove that for sufficiently large $m$ with $m=|V|-1$,
there exists a $\mathbf{T}$-transversal Hamilton path. Moreover, if $m=|V|$ and
at least $m-1$ of the tournaments $T_1,\ldots,T_m$ are assumed to be strongly
connected, then there is a $\mathbf{T}$-transversal Hamilton cycle. In our
proof, we utilize a novel way of partitioning tournaments which we dub
$\mathbf{H}$-partition.
