Planar Crossing Numbers of Genus g Graphs
نویسندگان
چکیده
Pach and Tóth [15] proved that any n-vertex graph of genus g and maximum degree d has a planar crossing number at most cdn, for a constant c > 1. We improve on this results by decreasing the bound to O(dgn), if g = o(n), and to O(g), otherwise, and also prove that our result is tight within a constant factor.
منابع مشابه
Planar Crossing Numbers of Graphs of Bounded Genus
Pach and Tóth proved that any n-vertex graph of genus g and maximum degree d has a planar crossing number at most cdn, for a constant c > 1. We improve on this results by decreasing the bound to O(dgn), and also prove that our result is tight within a constant factor. Our proof is constructive and yields an algorithm with time complexity O(dgn). As a consequence of our main result, we show a re...
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تاریخ انتشار 2006