Fast parallel algorithms for chordal graphs

We present an NC algorithm for recognizing chordal graphs, and we present NC algorithms for finding the following objects on chordal graphs: all maximal cliques, an intersection graph representation, an optimal coloring, a perfect elimination scheme, a maximum independent set, a minimum clique cover, and the chromatic polynomial. The well known polynomial algorithms for these problems seem highly sequential, and therefore a different approach is needed to find parallel algorithms.