Eulerian-spanning set and coboundary operator: An investigation of maxcut beyond planar graphs
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914620490383360 |
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| author | Fang, Qiming Shao, Sihong Wu, Yuxuan |
| author_facet | Fang, Qiming Shao, Sihong Wu, Yuxuan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_00725 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eulerian-spanning set and coboundary operator: An investigation of maxcut beyond planar graphs Fang, Qiming Shao, Sihong Wu, Yuxuan Data Structures and Algorithms Combinatorics 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. |
| title | Eulerian-spanning set and coboundary operator: An investigation of maxcut beyond planar graphs |
| topic | Data Structures and Algorithms Combinatorics |
| url | https://arxiv.org/abs/2606.00725 |