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arXiv · 2111.00721

Online Edge Coloring via Tree Recurrences and Correlation Decay

Janardhan Kulkarni·Yang P. Liu·Ashwin Sah·Mehtaab Sawhney·Jakub Tarnawski
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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.

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Janardhan Kulkarni, Yang P. Liu, Ashwin Sah, Mehtaab Sawhney, Jakub Tarnawski. 2021-11-01. Online Edge Coloring via Tree Recurrences and Correlation Decay. https://arxiv.org/abs/2111.00721

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