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dc.contributor.authorSobchuk, Mariia
dc.date.accessioned2019-08-28 18:24:39 (GMT)
dc.date.available2019-08-28 18:24:39 (GMT)
dc.date.issued2019-08-28
dc.date.submitted2019-08-27
dc.identifier.urihttp://hdl.handle.net/10012/14980
dc.description.abstractIn this thesis we are studying the cases when quantum independence and quantum chromatic numbers coincide with or differ from their classical counterparts. Knowing about the relation of chromatic numbers separation to the projective Kochen-Specker sets, we found an analogous characterisation for the independence numbers case. Additionally, all the graphs that we studied that had known quantum parameters exhibited both the separation between the classical and quantum independence numbers and the separation between the classical and quantum chromatic numbers. This observation and the Kochen-Specker connection suggested the possibility of the chromatic and independence numbers separations occurring simultaneously. We have disproved this idea with a counterexample. Furthermore, we generalised Manĉinska-Roberson’s example of the chromatic numbers separation to an infinite family. We investigate some known instances with strictly larger quantum independence numbers in-depth, find a more general description and generalise Piovesan’s example. Using the Lovász theta bound, we prove that there is no separation between the independence numbers in bipartite and perfect graphs. We also show that there is no separation when the classical independence number is two; and that the cone over a graph has the same quantum independence number as the underlying graph.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectQuantumen
dc.subjectChromaticen
dc.subjectNumberen
dc.subjectGraph theoryen
dc.subjectIndpendenceen
dc.subjectNumberen
dc.subjectCocliqueen
dc.subjectKochenen
dc.subjectSpeckeren
dc.subjectErdosen
dc.subjectRenyien
dc.subjectSeparationen
dc.titleQuantum independence and chromatic numbersen
dc.typeMaster Thesisen
dc.pendingfalse
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimizationen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorGodsil, Chris
uws.contributor.affiliation1Faculty of Mathematicsen
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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