The independence complex of a chordal graph is known to be shellable which 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. Moreover, we give a new proof of such result which yields different shellings of the independence complex.
"On the cover ideals of chordal graphs,"
Turkish Journal of Mathematics: Vol. 43:
5, Article 28.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss5/28