On-line list coloring of matroids

A coloring of a matroid is proper if elements of the same color form an independent set. A theorem of Seymour asserts that a k-colorable matroid is also colorable from any lists of size k. We prove an on-line version of this theorem. That is, a coloring from lists of size k of a k-colorable matroid is possible, even if appearances of colors in the lists are recovered color by color by an adversary, while our job is to assign a color immediately after it is recovered. (C) 2016 Elsevier B.V. All rights reserved.