A new result on Chvátal's conjecture

AbstractLet I be an ideal in 2[n] which is compressed with respect to a given element. We show that among the largest intersecting families of I there is always a star, as conjectured by Chvátal. As an easy corollary we obtain a result of Schönheim. We also show that if an ideal I has a basis B1,…, Bq such that the Bi can be partitioned into two 1-stars, then I satisfies Chvátal's conjecture