Improved Edge-Coloring Algorithms for Planar Graphs

Abstract We consider the problem of edge-coloring planar graphs. It is known that a planar graph G with maximum degree Δ ≥ 8 can be colored with Δ colors. We present two algorithms which find such a coloring when Δ ≥ 9. The first one is a sequential O(n log n) time algorithm. The other one is a parallel EREW PRAM algorithm which works in time O(log3n) and uses O(n) processors.

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