702 1 archive 2 disk0/00/00/07/02 2006-02-22 2008-09-18 11:09:00 2008-09-18 11:09:00 confpaper show 0 It is shown that if a graph of n vertices can be drawn on the torus without edge crossings and the maximum degree of its vertices is at most d, then its planar crossing number cannot exceed c_dn, where c_d is a constant depending only on d. This bound, conjectured by Brass, cannot be improved, apart from the value of the constant. We strengthen and generalize this result to the case when the graph has a crossing-free drawing on an orientable surface of higher genus and there is no restriction on the degrees of the vertices. http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=3843&spage=334 Pach János Tóth Géza September 12-14, 2005 Graph Drawing Limerick, Ireland Healy Patrick Healy, Patrick Nikolov Nikola S. Nikolov, Nikola S. pub 334-342 FALSE Springer FALSE G. Cairns and Y. Nikolayevsky.: Bounds for generalized thrackles, Discrete Comput. Geom., 23 (2000), 191--206. B. Mohar and C. Thomassen.: Graphs on surfaces, Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD, 2001. G. Salazar and E. Ugalde: An improved bound for the crossing number of C\sb m\times C\sb n: a self-contained proof using mostly combinatorial arguments, Graphs Combin., 20 (2004), 247--253. G.420 Z.1 published 2006 none