Deterministic and randomized online edge-coloring algorithms achieve (1+o(1))Delta colors for Delta=omega(log n) and Delta=omega(sqrt(log n)), respectively, matching Bar-Noy-Motwani-Naor lower bounds.
The greedy algorithm is optimal for on-line edge coloring
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Online Edge Coloring: Sharp Thresholds
Deterministic and randomized online edge-coloring algorithms achieve (1+o(1))Delta colors for Delta=omega(log n) and Delta=omega(sqrt(log n)), respectively, matching Bar-Noy-Motwani-Naor lower bounds.