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. We give an online algorithm that with high probability computes a \ ( (ee-1 + o (1) ) \) edge coloring on a graph \ (G\) with maximum degree \ (= (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 recurrence based approach for arguing correlation decay. Keywordsedge coloringonline algorithmstree recurrencescorrelation decayMSC codes68W2768R01
Kulkarni et al. (Mon,) studied this question.