Enoős' Problems and results in graph theory and combinatorial analysis, Proc, Fifth Britísh Com
- P. 2j
-. L9t F_be a family of-k-subsets of an rr-set. Let s be a fixed integer satisfying k<s=3k. Suppose that for Fl,F2,&€g lp'uaunl=s implies FanFze|4#g. katona asktd what is the maximum cardinality, Í'@,k,s'} of such a system. The Erdős-Ko-Rado theorem implies /-_1\ Ív'k,s):[í-iJ "' s:3k and n=2k. Inthis paper we show that f (n,k'"):Íí:1lholdsfor nrno(k) if and only if s>2k. Equality holds only if every nrember of F contains a fixed element of the underlying set. Furtherwesolvetheproblemfor k:3,s:-5,n=3000. Thisresultsharpensatheoremof Bo||obás.