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We present a new proof of a theorem of Erd˝ os, 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 ∆. Our proof yields the first-known linear-time algorithm to ∆-list-color graphs satisfying the hypothesis of the theorem.… (More)

We present a linear time algorithm to properly color the edges of any graph of maximum degree 3 using 4 colors. Our algorithm uses a greedy approach and utilizes a new structure theorem for such graphs.

We present efficient algorithms for three coloring problems on subcubic graphs. (A subcubic graph has maximum degree at most three.) The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. The second algorithm is the first randomized EREW PRAM… (More)

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