... and Schreiber [14] The existence of efficient Covering designs of complete hypergraphs was first proved by R¨dl in [13] o Our main result is that H -covering designs of Kn , having these three properties, ... edges of the form (ai , aj ), (ak , al ) in every member of L1 Thus there are r−1 3k h−1 h−1 such pairs in all the members of L1 Therefore, if µ is the expected number of Dπ -bad pairs, then ... pairs of adjacent edges of the form (ai , aj ), (ai , al ) in every member of L1 r−1 Thus, there are k h−1 (h − 1)(h − 2)(h − 3)/2 such pairs in all the members of L1 There are h−1 pairs of two...