Martin Grüttmüller

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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 6⊆ 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)
This paper deals with completion of partial latin squares L = (lij) of order n with k cyclically generated diagonals (li+t,j+t = lij + t if lij is not empty; with calculations modulo n). There is special emphasis on cyclic completion. Here, we present results for k = 2, . . . , 7 and odd n ≤ 21, and we describe the computational method used (hill-climbing).(More)
A balanced incomplete block design BIBD(v, k, λ) is a pair (V,B) where V is a v-set (points) and B is a collection of k-subsets of V (blocks) such that each pair of elements of V occurs in exactly λ blocks. A k-tournament is a directed graph on k vertices in which there is exactly one arc between any two distinct vertices. Given a k-tournament T , we call a(More)
A mandatory representation design MRD(K ; v) is a pairwise balanced design on v points with block sizes from the set K in which for each k ∈ K there is at least one block in the design of size k. In this paper, we consider MRDs with K = {4, k}, where k ≡ 2 mod 3, k ≥ 5, and prove that the necessary conditions for existence are sufficient if v ≡ 2 mod 3 and(More)