  An $r$-edge coloring of a graph or hypergraph $G=(V,E)$ is a map $c:E\to \{0,
\dots, r-1\}$. Extending results of Rado and answering questions of Rado,
Gy\'arf\'as and S\'ark\"ozy we prove that
  (1.) the vertex set of every $r$-edge colored countably infinite complete
$k$-uniform hypergraph can be partitioned into $r$ monochromatic tight paths
with distinct colors (a tight path in a $k$-uniform hypergraph is a sequence of
distinct vertices such that every set of $k$ consecutive vertices forms an
edge),
  (2.) for all natural numbers $r$ and $k$ there is a natural number $M$ such
that the vertex set of every $r$-edge colored countably infinite complete graph
can be partitioned into $M$ monochromatic $k^{th}$ powers of paths apart from a
finite set (a $k^{th}$ power of a path is a sequence $v_0, v_1, \dots$ of
distinct vertices such that $1\le|i-j| \le k$ implies that $v_iv_j$ is an
edge),
  (3.) the vertex set of every $2$-edge colored countably infinite complete
graph can be partitioned into $4$ monochromatic squares of paths, but not
necessarily into $3$,
  (4.) the vertex set of every $2$-edge colored complete graph on $\omega_1$
can be partitioned into $2$ monochromatic paths with distinct colors.
