A topological graph G is a graph drawn in the plane so that its edges are represented by Jordan arcs. G is called simple, if any two edges have at most one point in common. It is shown that the maximum number of edges of a simple topological graph with n vertices and no k pairwise disjoint edges is O (n log4k-8 n) edges. The assumption that G is simple cannot be dropped: for every n, there exists a complete topological graph of n vertices, whose any two edges cross at most twice. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Pach, J., & Tóth, G. (2005). Disjoint edges in topological graphs. In Lecture Notes in Computer Science (Vol. 3330, pp. 133–140). Springer Verlag. https://doi.org/10.1007/978-3-540-30540-8_15
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