  We extend results of Gy\'arf\'as and F\"uredi on the largest monochromatic
component in $r$-colored complete $k$-uniform hypergraphs to the setting of
random hypergraphs. We also study long monochromatic loose cycles in
$r$-colored random hypergraphs. In particular, we obtain a random analog of a
result of Gy\'arf\'as, S\'ark\"ozy, and Szemer\'edi on the longest
monochromatic loose cycle in $2$-colored complete $k$-uniform hypergraphs.

Combinatorics