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.
Chordal graph, cover ideal, shellable, linear quotients, Betti numbers
"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