Existence of incomplete resolvable minimum coverings of pairs by triples

Abstract For given positive integers u and v with u≡v≡0 ( mod 6) , let IRC( u , v ) denote an incomplete resolvable minimum covering of pairs by triples of order u having a hole of size v . It is proved in this paper that there exists such an IRC( u , v ) if and only if u ⩾3 v .

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