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{\bf Raphael Yuster}
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{\bf Rainbow $H$-factors}
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An {\em $H$-factor} of a graph $G$ is a spanning subgraph of $G$ whose
connected components are isomorphic to $H$. Given a properly
edge-colored graph $G$, a {\em rainbow} $H$-subgraph of $G$ is an
$H$-subgraph of $G$ whose edges have distinct colors. A {\em rainbow
$H$-factor} is an $H$-factor whose components are rainbow
$H$-subgraphs. The following result is proved. If $H$ is any fixed
graph with $h$ vertices then every properly edge-colored graph with
$hn$ vertices and minimum degree $(1-1/\chi(H))hn+o(n)$ has a rainbow
$H$-factor.
\bye