While there have been many results on lower bounds for Max Cut in unweighted graphs, the only lower bound for non-integer weights is that by Poljak and Turz{\'{\i}}k (1986). In this paper, we launch an extensive study of lower bounds for Max Cut in weighted graphs. We introduce a new approach for obtaining lower bounds for Weighted Max Cut. Using it, Probabilistic Method, Vizing's chromatic index theorem, and other tools, we obtain several lower bounds for arbitrary weighted graphs, weighted graphs of bounded girth and triangle-free weighted graphs. We pose conjectures and open questions.

翻译：虽然关于无权重图最大割的下界已有大量研究成果，但针对非整数权重的唯一下界仍来自Poljak与Turzík（1986年）的工作。本文对加权图最大割的下界展开系统性研究，提出一种获取加权最大割下界的新方法。通过结合该方法、概率方法、Vizing色指数定理及其他工具，我们获得了任意加权图、有界围长加权图及无三角形加权图的若干下界。文末提出相关猜想与待解决问题。