A common generalization to strengthenings of Drisko's Theorem for intersections of two matroids

Eli Berger; Daniel McGinnis

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arXiv · 2511.03135

A common generalization to strengthenings of Drisko's Theorem for intersections of two matroids

Eli Berger·Daniel McGinnis

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Abstract

Let $\mathcal{M}$ and $\mathcal{N}$ be two matroids on the same ground set $V$. Let $A_1,\dots,A_{2n-1}$ be sets which are independent in both $\mathcal{M}$ and $\mathcal{N}$, satisfying $|A_i|\geq \textrm{min}(i,n)$ for all $i$. We show that there exists a partial rainbow set of size $n$, which is independent in both $\mathcal{M}$ and $\mathcal{N}$. This is a common generalization of rainbow matching results for bipartite graphs by Aharoni, Berger, Kotlar, and Ziv, and for the intersection of two matroid by Kotlar and Ziv.

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BibTeX RIS

Eli Berger, Daniel McGinnis. 2025-11-05. A common generalization to strengthenings of Drisko's Theorem for intersections of two matroids. https://arxiv.org/abs/2511.03135

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