Coloring the intersection of two matroids
Eli Berger, He Guo · Proceedings of the American Mathematical Society · 2025
A result from Aharoni and the first author of this paper [Trans. Amer. Math. Soc. 358 (2006), pp. 4895–4917] states that for any two positive integers p , q p,q , where p p divides q q , if a matroid M \mathcal {M} is p p -colorable and a matroid N \mathcal {N} is q q -colorable then M ∩ N \mathcal {M}\cap \mathcal {N} is ( p + q ) (p+q) -colorable. In this paper we show that the assumption that p p divides q q is in fact redundant, and we also prove that M ∩ N \mathcal {M}\cap \mathcal {N} is even p + q p+q list-colorable. The result uses topology and relies on a new parameter yielding a lower bound for the topological connectivity of the intersection of two matroids.