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- W2614458809 abstract "Research about crossings is typically about minimization. In this paper, we consider maximizing the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a convex straight-line drawing, that is, a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard." @default.
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- W2614458809 date "2018-01-01" @default.
- W2614458809 modified "2023-10-01" @default.
- W2614458809 title "On the Maximum Crossing Number" @default.
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- W2614458809 doi "https://doi.org/10.1007/978-3-319-78825-8_6" @default.
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