In sec tion 1, transversal Inatroids are assoc iated with "syste ms of di s tinct represe ntatives" (i. e., tra nsversals) and,. more generally , matc hing matroids are associated with matc hings in graphs . Th e transversal matrolds and a theore m of P. J. Higgins on disjoint transversals of a famil y of se ts , along wIth th e well-known graphIc matrold s a nd some theorems on decomposition o...

A transversal of a family .Fof sets is a family of pairwise distinct elements, one from each member of .y , and a multitransversal of .IF is a family of pairwise disjoint subsets, one of each member of F . The main result of this note, Theorem 4, gives necessary and sufficient conditions on families sa/ and .4 of cardinals in order that every family J whose members have cardinals given by sl sh...

For any graph, there is a largest integer k such that given any partition of the vertex set with at most k elements in each class of the partition, there is transversal of the partition that is a dominating set in the graph. Some basic results about this parameter, the partition domination number, are obtained. In particular, it is shown that its value is 2 for the two-dimensional infinite grid...

The paper deals with m by n rectangular arrays whose mn cells are filled with symbols. A section of the array consists of m cells, one from each row and no two from the same column. The paper focuses on the existence of sections that do contain symbols with high multiplicity.

Call an hypergraph, that is a family of subsets (edges) from a finite vertex set, an exact transversal hypergraph iff each of its minimal transversals, i.e., minimal vertex subsets that intersect each edge, meets each edge in a singleton. We show that such hypergraphs are recognizable in polynomial time and that their minimal transversals as well as their maximal independent sets can be generat...