Maximum degree and fractional matchings in uniform hypergraphs

--avs subject classification (1980): 05 C 65, 05 C 35; 05 B 25 Let 3f be a family of r-subsets of a finite set X. Set D(/{):max|{E: xQE€lf,}|, (maximum degree). We say that 3/f, is intersecting if for any H, H,€;( .we Itave _H ) E, #0. In this case, obuiő".rí, ottj=tcfÍh. According to a well-known conjec1ule D9r)=|ű.|l(r-|*1lr). We proveísügiítiíströnger result .Let /f, beanr-uniform, intersecting hypergraph. Then either it is a pro. jective pla]ne ór oroú r-1, consaquently D(/f,):|af,|l.?_1*1lr), ot. D(/f)=l/(|l(r-1)' This i. a co.ölla'y to a more general theórem on nó| necessarily intersecting hypergraphs.