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Bounded-Defect Proper Orientations and Graphs on Surfaces
Chen, Mohar and Wu [J. Combin. Theory Ser. B 161 (2023)] conjectured that every graph of orientable genus $g$ has proper orientation number $O(\sqrt g)$. We prove this conjecture. Our main result extends the potential-outdegree method from independent color classes to three parts of bounded internal
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