On-line list coloring of matroids

Lason, Michael; Lubawski, Wojciech (2017). On-line list coloring of matroids. Discrete applied mathematics, 217(part 2), pp. 353-355. Elsevier 10.1016/j.dam.2016.08.002

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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.

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