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We study maximal families A of subsets of [n] = {1, 2,. .. , n} such that A contains only pairs and triples and A ⊆ B for all {A, B} ⊆ A, i.e. A is an antichain. For any n, all such families A of minimum size are determined. This is equivalent to finding all graphs G = (V, E) with |V | = n and with the property that every edge is contained in some triangle(More)
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Abstract. Possibility theory is applied to introduce and reason about the fundamental notion of a key for uncertain data. Uncertainty is modeled(More)
We consider the poset of all submatrices of a given matrix, ordered by containment. The unique rank function for this poset is given by r(M) = R(M)+C(M)?1, where R(M) and C(M) denote the number of rows and columns of a nonempty matrix M, respectively, and the rank of the empty matrix is 0. For xed k and i our objective is to nd a set M of submatrices M 1 ;(More)
Let n be a natural number and C = fP 0 ; : : :; P n-1 g a collection of spanning subgraphs of K n , the complete graph on n vertices. C is called an Orthogonal Double Cover (ODC) if every edge of K n belongs to exactly two elements of C and every two elements of C have exactly one edge in common. Gronau, Mullin and Schellenberg showed that the complete(More)
It is proved that, for any positive integer m, the weight of the union-closure of any m distinct 2-sets is at least as large as the weight of the union-closure of the first m 2-sets in squashed (antilexicographic) order, where all i-sets have the same non-negative weight w i with w i ≤ w i+1 for all i, and the weight of a family of sets is the sum of the(More)