A.E. Kézdy and H.S. Snevily, On Extensions of a Conjecture of Gallai, J. Combin. Theory Ser. B 70 (1997), 317-324.
Abstract: A graph G is k-critical if it has chromatic number k but every proper subgraph of G has a (k-1)-coloring. We prove the following result. If G is a k-critical graph of order n > k ≥ 3, then G contains fewer than n - 3k/5 + 2 complete subgraphs of order k-1.
The conjecture by Abbott and Zhou suggests that G contains at most n-k+3 complete subgraphs of order k-1, and they proved this for k=4.
August 18, 1997. B. Toft.