?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Crossing+number+of+toroidal+graphs&rft.creator=Pach%2C+J%C3%83%C2%A1nos&rft.creator=T%C3%83%C2%B3th%2C+G%C3%83%C2%A9za&rft.subject=G.420+Crossings&rft.subject=Z.001+General&rft.description=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%2C+then+its+planar+crossing+number+cannot+exceed+c_dn%2C+where+c_d+is+a+constant+depending+only+on+d.+This+bound%2C+conjectured+by+Brass%2C+cannot+be+improved%2C+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.%0D%0A++++&rft.publisher=Springer&rft.contributor=Healy%2C+Patrick&rft.contributor=Nikolov%2C+Nikola+S.&rft.date=2006&rft.type=Conference+Paper&rft.type=NonPeerReviewed&rft.identifier=Pach%2C+J%C3%83%C2%A1nos+and+T%C3%83%C2%B3th%2C+G%C3%83%C2%A9za+(2006)+Crossing+number+of+toroidal+graphs.+[Conference+Paper]&rft.relation=http%3A%2F%2Fgdea.informatik.uni-koeln.de%2F702%2F