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Finding a maximum cardinality common independent set in two matroids (alsoknown as Matroid Intersection) is a classical combinatorial optimizationproblem, which generalizes several well-known problems, such as finding amaximum bipartite matching, a maximum colorful forest, and an arborescence indirected graphs. Enumerating all maximal common independent sets in two (ormore) matroids is a classical enumeration problem. In this paper, we address an``intersection'' of these problems: Given two matroids and a threshold $\tau$,the goal is to enumerate all maximal common independent sets in the matroidswith cardinality at least $\tau$. We show that this problem can be solved inpolynomial delay and polynomial space. We also discuss how to enumerate allmaximal common independent sets of two matroids in non-increasing order oftheir cardinalities.

Polynomial-Delay Enumeration of Large Maximal Common Independent Sets in Two Matroids