Online Edge Coloring via Tree Recurrences and Correlation Decay

Abstract

We give an online algorithm that with high probability computes a $\left(\frac{e}{e-1}+o(1)\right)\Delta$ edge coloring on a graph $G$ with maximum degree $\Delta =\omega (\log n)$ 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.

22 pages, 1 figure