Eulerian-spanning set and coboundary operator: An investigation of maxcut beyond planar graphs
This provides a new algorithmic approach for maxcut beyond planar graphs, offering a fixed-parameter tractable solution for graphs with bounded crossing number.
The authors generalize Hadlock's maxcut conversion from planar to general graphs using Eulerian-spanning sets and coboundary operators, yielding an FPT algorithm for k-contraction apex graphs that runs in O(2^k (n+k)^{3/2} log(n+k)) time, matching best known results for non-negative weights.
Using the concepts of Eulerian-spanning set and coboundary operator, we generalize Hadlock's conversion of the maxcut problem on planar graphs to one on general graphs with non-negative weights. Using our conversion, we can explore algorithms for maxcut beyond the class of planar graphs. We obtain a Fixed-Parameter Tractable algorithm for $k$-contraction apex graphs. Specifically, our algorithm can be applied to graphs with crossing number $k$, giving an $O(2^k(n+k)^{3/2}\log (n+k))$-time algorithm that matches the best known results when restricted to non-negative weights.