Using results from extremal graph theory, we determine the asymptotic number of string graphs with n vertices, i.e., graphs that can be obtained as the intersection graph of a system of continuous arcs in the plane. The number becomes much smaller, for any fixed d, if we restrict our attention to systems of arcs, any two of which cross at most d times. As an application, we estimate the number of different drawings of the complete graph Kn with n vertices under various side conditions. © Springer-Verlag 2004.
CITATION STYLE
Pach, J., & Tóth, G. (2004). How Many Ways Can One Draw a Graph? Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2912, 47–58. https://doi.org/10.1007/978-3-540-24595-7_5
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