Abstract
Pach and Tóth [14] proved that any n-vertex graph of genus g and maximum degree d has a planar crossing number at most c g dn, 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 2), otherwise, and also prove that our result is tight within a constant factor.
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Djidjev, H., Vrt’o, I. (2006). Planar Crossing Numbers of Genus g Graphs. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_37
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DOI: https://doi.org/10.1007/11786986_37
Publisher Name: Springer, Berlin, Heidelberg
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