Extensions of the Erdős-Ko-Rado Theorem to Perfect Matchings

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dc.contributor.advisorMeagher, Karen
dc.contributor.advisorFallat, Shaun
dc.contributor.authorNasrollahi Shirazi, Mahsa
dc.contributor.committeememberHerman, Allen
dc.contributor.committeememberZilles, Sandra
dc.contributor.committeememberNasserasr, Shahla
dc.contributor.externalexaminerGuo, Krystal
dc.date.accessioned2022-08-05T15:18:24Z
dc.date.available2022-08-05T15:18:24Z
dc.date.issued2022-03-31
dc.descriptionA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics, University of Regina. x, 107 p.en_US
dc.description.abstractOne of the important results in extremal set theory is the Erdős-Ko-Rado (EKR) theorem which gives a tight upper bound on the size of intersecting sets. The focus of this thesis is on extensions of the EKR theorem to perfect matchings and uniform set partitions. Two perfect matchings are said to be t-intersecting if they have at least t edges in common. In 2017, Godsil and Meagher algebraically proved the EKR theorem for intersecting perfect matchings on the complete graph with 2k vertices. In 2017, Lindzey presented an asymptotic refinement of the EKR theorem on perfect matchings. In this thesis, we extend their results to 2-intersecting and also to set-wise 2-intersecting perfect matchings. These results are not asymptotic. A perfect matching is in fact a special case of a uniform set partition. Another focus of this thesis is on partially 2-intersecting uniform set partitions. We find the largest set of 2-intersecting uniform set partitions, when the number of parts is sufficiently large. The result on uniform set partitions is part of a joint research project with Karen Meagher and Brett Stevens.en_US
dc.description.authorstatusStudenten
dc.description.peerreviewyesen
dc.identifier.tcnumberTC-SRU-14948
dc.identifier.thesisurlhttps://ourspace.uregina.ca/bitstream/handle/10294/14948/Nasrollahi_Shirazi_Mahsa_Phd_MATH_Spring_2022.pdf
dc.identifier.urihttps://hdl.handle.net/10294/14948
dc.language.isoenen_US
dc.publisherFaculty of Graduate Studies and Research, University of Reginaen_US
dc.titleExtensions of the Erdős-Ko-Rado Theorem to Perfect Matchingsen_US
dc.typeThesisen_US
thesis.degree.departmentDepartment of Mathematics and Statisticsen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Reginaen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophy (PhD)en_US
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