Online Edge Coloring via Tree Recurrences and Correlation Decay
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We give an online algorithm that with high probability computes a (e/e-1 + o(1))Δ edge coloring on a graph G with maximum degree Δ = ω(log n) under online edge arrivals against oblivious adversaries, making first progress on the conjecture of Bar-Noy, Motwani, and Naor in this general setting. Our algorithm is based on reducing to a matching problem on locally treelike graphs, and then applying a tree recurrences based approach for arguing correlation decay.
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