Online Edge Coloring via Tree Recurrences and Correlation Decay - Kulkarni, Janardhan (Jana); Liu, Yang; Liu, Yang; Liu, Yang; Sah, Ashwin; Sawhney, Mehtaab; Tarnawski, Jakub (STOC 2022, 2022)
We give an online algorithm that with high probability computes a edge coloring on a graph with maximum degree 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.