Abstract
We present efficient algorithms for three coloring problems on subcubic graphs (ones with maximum degree 3). These algorithms are based on a simple decomposition principle for subcubic graphs. 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. As evidence we give the first randomized EREW PRAM algorithm that uses O(n/log n) processors and runs in O(log n) time with high probability, where n is the number of vertices of the input graph. The second algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The third algorithm generalizes this to the first linear-time algorithm to 5-list-total-color subcubic graphs.
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