“…Mubayi and Verstraëte [17] proved the conjecture for all k ≥ 3 and d = 2. Recently, Currier [4] proved this conjecture for all k ≥ d + 1 ≥ 3 and n ≥ 2k. The Chvátal Simplex Conjecture is still open in general for n < 2k and 3 ≤ d ≤ k − 2, and we refer the reader to [1,3,8,5,6,12,13,15] and their references for more results related to this conjecture.…”