“…The first goes back to the 'nibble' (semi-random) method of Rödl [90], introduced to solve the Erdős-Hanani [26] conjecture on approximate Steiner systems (see the next section), which has since had a great impact on Combinatorics (e.g. [5,10,11,12,13,14,28,29,38,50,51,66,69,76,85,99,104]). A special case of a theorem of Kahn [51] is that if there is a fractional perfect matching on the edges of an r-graph G on [n] such that for any pair of vertices x, y the total weight on edges containing {x, y} is o(1) then G has a matching covering all but o(n) vertices.…”