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{\bf Ryan Martin and Yi Zhao}
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{\bf Tiling Tripartite Graphs with $3$-Colorable Graphs}
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For any positive real number $\gamma$ and any positive integer $h$, there
is $N_0$ such that the following holds. Let $N\ge N_0$ be such that
$N$ is divisible by $h$. If $G$ is a tripartite graph with $N$
vertices in each vertex class such that every vertex is adjacent to at
least $(2/3+ \gamma) N$ vertices in each of the other classes, then $G$
can be tiled perfectly by copies of $K_{h,h,h}$.  This extends the
work in [Discrete Math. {\bf254} (2002), 289--308] and also gives a
sufficient condition for tiling by any fixed 3-colorable
graph. Furthermore, we show that the minimum-degree $(2/3+ \gamma) N$ in
our result cannot be replaced by $2N/3+ h-2$.

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