  In this note, we describe a $\alpha_{GW} + \tilde{\Omega}(1/d^2)$-factor
approximation algorithm for Max-Cut on weighted graphs of degree $\leq d$.
Here, $\alpha_{GW}\approx 0.878$ is the worst-case approximation ratio of the
Goemans-Williamson rounding for Max-Cut. This improves on previous results for
unweighted graphs by Feige, Karpinski, and Langberg and Flor\'en. Our guarantee
is obtained by a tighter analysis of the solution obtained by applying a
natural local improvement procedure to the Goemans-Williamson rounding of the
basic SDP strengthened with triangle inequalities.
