  The independence complex of a chordal graph is known to be shellable due to a
result of Van Tuyl and Villarreal. This is equivalent to the fact that cover
ideal of a chordal graph has linear quotients. We use this result to obtain
recursive formulas for the Betti numbers of cover ideals of chordal graphs.
Also, we give a new proof of their result which yields different shellings of
the independence complex.
