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Information Processing Letters
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We present a new proof of a theorem of Erd枚s, Rubin, and Taylor, which states that the list chromatic number (or choice number) of a connected, simple graph that is neither complete nor an odd cycle does not exceed its maximum degree 驴. Our proof yields the first-known linear-time algorithm to 驴list-color graphs satisfying the hypothesis of the theorem. Without change, our algorithm can also be used to 驴 color such graphs. It has the same running time as, but seems to be much simpler than, the current known algorithm, due to Lov谩sz, for 驴 coloring such graphs. We also give a specialized version of our algorithm that works on subcubic graphs (ones with maximum degree three) by exploiting a simple decomposition principle for them.