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Rota's Basis Conjecture holds asymptotically
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classification
math.CO
keywords
basesbasisconjecturedisjointmatroidpossiblerainbowrota
abstract
Rota's Basis Conjecture is a well known problem from matroid theory, that states that for any collection of $n$ bases in a rank $n$ matroid, it is possible to decompose all the elements into $n$ disjoint rainbow bases. Here an asymptotic version of this is proved. We show that it is possible to find $n-o(n)$ disjoint rainbow independent sets of size $n-o(n)$.
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