{"ID":2922092,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-02T13:21:47.35720266Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.00725","arxiv_id":"2606.00725","title":"Eulerian-spanning set and coboundary operator: An investigation of maxcut beyond planar graphs","abstract":"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.","short_abstract":"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 Tra...","url_abs":"https://arxiv.org/abs/2606.00725","url_pdf":"https://arxiv.org/pdf/2606.00725v1","authors":"[\"Qiming Fang\",\"Sihong Shao\",\"Yuxuan Wu\"]","published":"2026-05-30T13:33:40Z","proceeding":"cs.DS","tasks":"[\"cs.DS\",\"math.CO\"]","methods":"[]","has_code":false}