Obstructions for local tournament orientation completions

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dc.contributor.authorHsu, Kevin
dc.contributor.supervisorHuang, Jing
dc.date.accessioned2020-08-24T06:18:28Z
dc.date.available2020-08-24T06:18:28Z
dc.date.copyright2020en_US
dc.date.issued2020-08-23
dc.date.issued2020-08-23
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractThe orientation completion problem for a hereditary class C of oriented graphs asks whether a given partially oriented graph can be completed to a graph belonging to C. This problem was introduced recently and is a generalization of several existing problems, including the recognition problem for certain classes of graphs and the representation extension problem for proper interval graphs. A local tournament is an oriented graph in which the in-neighbourhood as well as the out-neighbourhood of each vertex induces a tournament. Local tournaments are a well-studied class of oriented graphs that generalize tournaments and their underlying graphs are intimately related to proper circular-arc graphs. Proper interval graphs are precisely those which can be oriented as acyclic local tournaments. The orientation completion problems for the class of local tournaments and the class of acyclic local tournaments have been shown to be polynomial-time solvable. In this thesis, we characterize the partially oriented graphs that can be completed to local tournaments by finding a complete list of obstructions. These are in a sense the minimal partially oriented graphs that cannot be completed to local tournaments. We also determine the minimal partially oriented graphs that cannot be completed to acyclic local tournaments.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.bibliographicCitationKevin Hsu and Jing Huang. Obstructions for acyclic local tournament orientation completions. arXiv e-prints, page arXiv:2008.07104, August 2020.en_US
dc.identifier.urihttp://hdl.handle.net/1828/12024
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectgraph theoryen_US
dc.subjectmathematicsen_US
dc.subjectdiscrete mathematicsen_US
dc.subjectgraph orientationsen_US
dc.subjectproper interval graphsen_US
dc.subjectproper circular-arc graphsen_US
dc.subjectlocal tournamentsen_US
dc.subjectacyclic local tournamentsen_US
dc.subjectorientation completion problemen_US
dc.subjectcombinatoricsen_US
dc.titleObstructions for local tournament orientation completionsen_US
dc.typeThesisen_US

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