Talk:Partition matroid

In the definition section, the article says : "A basis of the matroid is a set whose intersection with every block B_i has size exactly d_i."

Is really the size required to be *exactly* d_i, or rather at most d_i (with extra constraints on global maximality). For example for the Max Matching problem, a bipartite graph might be such that some vertices have degree 0 (and thus no selectable edges), while the problem is formulated in terms of matroid intersection with d_i=1. Or am I missing something?

Acasteigts (talk) 14:17, 12 November 2017 (UTC)[reply]

Bipartite maximum matching is a matroid intersection problem where you're trying to find a largest set that's independent in two matroids. It is not necessarily a basis in either of them. The exactness condition is only for bases, not for independent sets, as it says. —David Eppstein (talk) 17:06, 12 November 2017 (UTC)[reply]