Abstract: Schaffer and Yannakakis have shown that the max-cut problem with the FLIP neighborhood is polynomial-time local search (PLS) complete, and hence among the most difficult problems in the PLS class. The FLIP neighbourhood of a 2-partition is defined by moving a single vertex to the opposite class. In this paper, the author has shown that when restricted to the cubic graph, the FLIP local search becomes "easy" and finds a local max-cut in $O(n^2)$ steps.
Paper Link: https://epubs.siam.org/doi/pdf/10.1137/S0097539793245350
