3 problems

Let ${\cal M}=(E,\mathcal{I})$ be a matroid. It is $k$-coverable if its ground set $E$ can be covered by at most $k$ independent sets from $\mathcal{I}$. A partition matroid on the…

Let $M$ be a matroid whose ground set can be covered by $k$ independent sets; such a matroid is $k$-coverable. A reduction of a matroid is the reduction notion used in the source,…

Let $M$ be a $k$-colorable matroid, meaning that its ground set can be partitioned into $k$ independent sets. A reduction to a partition matroid is a partition matroid on the same…