Show simple item record

dc.contributor.authorPan, Shengjunen
dc.date.accessioned2006-08-22 14:26:51 (GMT)
dc.date.available2006-08-22 14:26:51 (GMT)
dc.date.issued2006en
dc.date.submitted2006en
dc.identifier.urihttp://hdl.handle.net/10012/1174
dc.description.abstractIn this thesis we prove two main results. The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of <em>K<sub>n</sub></em> must be a triangle (for <em>n</em> &ge; 3). We prove that, for the larger class of pseudolinear drawings, the outer face must be a triangle. The other main result is the next step toward Guy's Conjecture that the crossing number of <em>K<sub>n</sub></em> is $(1/4)[n/2][(n-1)/2][(n-2)/2][(n-3)/2]$. We show that the conjecture is true for <em>n</em> = 11,12; previously the conjecture was known to be true for <em>n</em> &le; 10. We also prove several minor results.en
dc.formatapplication/pdfen
dc.format.extent414477 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2006, Pan, Shengjun. All rights reserved.en
dc.subjectMathematicsen
dc.subjectgraphen
dc.subjectcrossing numberen
dc.subjectGuy's Conjectureen
dc.titleOn the Crossing Numbers of Complete Graphsen
dc.typeMaster Thesisen
dc.pendingfalseen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record


UWSpace

University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages