A Matroid Generalization of a Result on Row-Latin Rectangles

Details A Matroid Generalization of a Result on Row-Latin Rectangles A Matroid Generalization of a Result on Row-Latin Rectangles

1998-07-08

arxiv.org/abs/math/9807036v1

Mathematics

Combinatorics

9 pages, 5 figures

Scientific paper

Let A be an m \times n matrix in which the entries of each row are all distinct. Drisko showed that, if m \ge 2n-1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in a matroid. For such a matrix A, we show that if each row of A forms an independent set, then we can require the transversal to be independent as well. We determine the complexity of an algorithm based on the proof of this result. Lastly, we observe that m \ge 2n-1 appears to force the existence of not merely one but many transversals. We discuss a number of conjectures related to this observation (some of which involve matroids and some of which do not).

Affiliated with

Also associated with

No associations

Rating

A Matroid Generalization of a Result on Row-Latin Rectangles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Matroid Generalization of a Result on Row-Latin Rectangles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Matroid Generalization of a Result on Row-Latin Rectangles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-607437