On the Length of a Partial Independent Transversal in a Matroidal Latin Square

Details On the Length of a Partial Independent Transversal in a Matroidal Latin Square On the Length of a Partial Independent Transversal in a Matroidal Latin Square

2012-04-24

arxiv.org/abs/1204.5274v1

Electronic J. Combinatorics, volume 19, Issue 2 (2012)

Mathematics

Combinatorics

Scientific paper

We suggest and explore a matroidal version of the Brualdi - Ryser conjecture
about Latin squares. We prove that any $n\times n$ matrix, whose rows and
columns are bases of a matroid, has an independent partial transversal of
length $\lceil2n/3\rceil$. We show that for any $n$, there exists such a matrix
with a maximal independent partial transversal of length at most $n-1$.

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