  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
Turzik (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.
