We provide a simple online $\Delta(1+o(1))$-edge-coloring algorithm for bipartite graphs of maximum degree $\Delta=\omega(\log n)$ under adversarial vertex arrivals on one side of the graph. Our algorithm slightly improves the result of (Cohen, Peng and Wajc, FOCS19), which was the first, and currently only, to obtain an asymptotically optimal $\Delta(1+o(1))$ guarantee for an adversarial arrival model. More importantly, our algorithm provides a new, simpler approach for tackling online edge coloring.

翻译：我们针对最大度Δ=ω(log n)的二部图，在单侧顶点对抗性到达的情况下，提出了一种简单的在线Δ(1+o(1))-边着色算法。该算法略微改进了(Cohen, Peng and Wajc, FOCS19)的结果——该结果是对抗性到达模型下首个且目前唯一获得渐近最优Δ(1+o(1))保证的算法。更重要的是，我们的算法为解决在线边着色问题提供了一种新的、更简洁的方法。