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- W1517436122 abstract "A drawing of a graph is x-monotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an x-monotone drawing in which every pair of edges crosses an even number of times, then the graph has an x-monotone embedding in which the x-coordinates of all vertices are unchanged. We give a new proof of this result and strengthen it by showing that the conclusion remains true even if adjacent edges are allowed to cross oddly. This answers a question posed by Pach and Tóth. Moreover, we show that an extension of this result for graphs with non-adjacent pairs of edges crossing oddly fails even if there exists only one such pair in a graph." @default.
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- W1517436122 date "2011-01-01" @default.
- W1517436122 modified "2023-10-03" @default.
- W1517436122 title "Hanani-Tutte and Monotone Drawings" @default.
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- W1517436122 doi "https://doi.org/10.1007/978-3-642-25870-1_26" @default.
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