Rota's Basis Conjecture for Matroids with Density Close to One

Published 14 Jul 2021 in math.CO | (2107.07024v3)

Abstract: Rota's basis conjecture (RBC) states that given a collection B of n bases in a matroid M of rank n, one can always find n disjoint rainbow bases with respect to B. We show that if M is a matroid having n + k elements, then one can construct n - k³ disjoint rainbow bases, where b is a constant depending only on k.

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Sean McGuinness

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