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Abstract:
A parallel (CRCW PRAM) algorithm is given to find a $k$-coloring of
a graph randomly drawn from the family of $k$-colorable graphs with
$n$ vertices, where $k = \log^{O(1)}n$. The average running time of
the algorithm is {\em constant}, and the number of processors is equal
to $|V|+|E|$, where $|V|$, $|E|$, resp. is the number of vertices,
edges, resp. of the input graph.
