Fixed-parameter algorithms for the weighted Max-Cut problem on embedded 1-planar graphs

We propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by crossing number k of given embedding. A graph is called if it can be drawn in plane with at most one per edge. Our recursively reduce a to 3k planar graphs, using edge removal and node contraction. main algorithm then solves FCE-MaxCut introduced Liers Pardella [23]. In case non-negative weights, we suggest variant that allows solve instances any algorithm. show maximum cut derived from solutions graphs. compute an n nodes crossings time O(3k⋅n3/2log⁡n).