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 $n-1$.
@article{10_37236_2229,
author = {Daniel Kotlar and Ran Ziv},
title = {On the length of a partial independent transversal in a matroidal {Latin} square},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {2},
doi = {10.37236/2229},
zbl = {1243.05051},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2229/}
}
TY - JOUR
AU - Daniel Kotlar
AU - Ran Ziv
TI - On the length of a partial independent transversal in a matroidal Latin square
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2229/
DO - 10.37236/2229
ID - 10_37236_2229
ER -
%0 Journal Article
%A Daniel Kotlar
%A Ran Ziv
%T On the length of a partial independent transversal in a matroidal Latin square
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2229/
%R 10.37236/2229
%F 10_37236_2229
Daniel Kotlar; Ran Ziv. On the length of a partial independent transversal in a matroidal Latin square. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2229
