ONLINE EDGE COLORING VIA TREE RECURRENCES AND CORRELATION DECAY\ast

We give an online algorithm that with high probability computes a ( e e - 1 + o(1))\Delta edge coloring on a graph G with maximum degree \Delta = \omega(logn) 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.