Before revision:  In their celebrated (p,q) theorem from 1992, Alon and Kleitman proved the conjecture but did not obtain effective bounds on c_d(p,q), called `the Hadwiger-Debrunner numbers' . Ever since, obtaining such bounds is a major open problem in convexity theory .
After revision:  In their celebrated (p,q) theorem from 1992, Alon and Kleitman proved the conjecture . However, obtaining sharp bounds on c_d(p,q), called `the Hadwiger-Debrunner numbers' . Ever since, obtaining such bounds is a major open problem in convexity theory .