Lower Bounds for Maximum Weighted Cut

TL;DR

This paper develops new lower bounds for the Max Cut problem in weighted graphs using probabilistic and combinatorial methods, expanding understanding beyond unweighted cases.

Contribution

It introduces a novel approach for deriving lower bounds in weighted Max Cut and explores bounds for various classes of weighted graphs.

Findings

Established new lower bounds for weighted Max Cut

Applied probabilistic and combinatorial tools to weighted graphs

Identified open problems and conjectures in the field

Abstract

While there have been many results on lower bounds for Max Cut in unweighted graphs, there are only few results for lower bounds for Max Cut in weighted graphs. 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.