We give the first efficient parallel algorithms for recognizing chorda
l graphs, finding a maximum clique and a maximum independent set in a
chordal graph, finding an optimal coloring of a chordal graph, finding
a breadth-first search tree and a depth-first search tree of a chorda
l graph, recognizing interval graphs, and testing interval graphs for
isomorphism. The key to our results is an efficient parallel algorithm
for finding a perfect elimination ordering.