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AuthorGentner, Michaeldc.contributor.author
Date of accession2018-02-07T07:28:52Zdc.date.accessioned
Available in OPARU since2018-02-07T07:28:52Zdc.date.available
Year of creation2017dc.date.created
Date of first publication2018-02-07dc.date.issued
AbstractThis thesis comprises the results of five research papers on domination and zero forcing. In "Largest Domination Number and Smallest Independence Number of Forests with given Degree Sequence" (Gentner, Henning, Rautenbach, 2016) and "Smallest Domination Number and Largest Independence Number of Graphs and Forests with given Degree Sequence" (Gentner, Henning, Rautenbach, 2017) we examine best possible bounds for the domination number, based on the degree sequence of a graph. In some cases these bounds coincide with the Slater number of the sequence, which is a simple lower bound for the domination number. In "Some Comments on the Slater number" (Gentner, Rautenbach, 2017), we explore some more results involving the Slater number. Particularly, we determine graph classes for which the domination number is bounded from above by a term that is linear in the Slater number. In "Extremal values and bounds for the zero forcing number" (Gentner, Penso, Souza, Rautenbach, 2016) we prove two conjectures on the zero forcing number. One of these conjectures is a special case of another one, which we partially prove in "Some Bounds on the Zero Forcing Number of a Graph" (Gentner, Rautenbach, 2016). Additionally, we establish further bounds for the zero forcing number using different techniques. Apart from these papers, we explain the original motivation for the zero forcing problem and its connection to domination. While the origins of zero forcing lie in algebraic graph theory and physics, a lot of other applications can be found. One of these is the power domination problem, which also establishes the connection between domination and zero forcing.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
Has partMichael Gentner, Michael A. Henning and Dieter Rautenbach, 2016, Largest Domination Number and Smallest Independence Number of Forests with given Degree Sequence, Discrete Applied Mathematics 206 pp.181-187, DOI: 10.1016/j.dam.2016.01.040dc.relation.haspart
Has partMichael Gentner, Michael A. Henning and Dieter Rautenbach, 2016, Smallest Domination Number and Largest Independence Number of Graphs and Forests with given Degree Sequence, Journal of Graph Theory, DOI: 10.1002/jgt.22189dc.relation.haspart
Has partMichael Gentner and Dieter Rautenbach, 2017, Some Comments on the Slater number, Discrete Mathematics 340 pp.1497-1502, DOI: 10.1016/j.disc.2017.02.009dc.relation.haspart
Has partMichael Gentner and Dieter Rautenbach, 2018, Some Bounds on the Zero Forcing Number of a Graph, Discrete Applied Mathematics 236 pp.203-213, DOI: 10.1016/j.dam.2017.11.015dc.relation.haspart
Has partMichael Gentner, Lucia D. Penso, Ueverton S. Souza, and Dieter Rautenbach, Extremal values and bounds for the zero forcing number, Discrete Applied Mathematics 214 pp.196-200, DOI: 10.1016/j.dam.2016.06.004dc.relation.haspart
LicenseStandarddc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v3dc.rights.uri
KeywordZero Forcingdc.subject
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHGraph theorydc.subject.lcsh
LCSHDomination (Graph theory)dc.subject.lcsh
TitleDomination and forcingdc.title
Resource typeDissertationdc.type
Date of acceptance2018-01-25dcterms.dateAccepted
RefereeRautenbach, Dieterdc.contributor.referee
RefereeBruhn-Fujimoto, Henningdc.contributor.referee
DOIhttp://dx.doi.org/10.18725/OPARU-5428dc.identifier.doi
PPN1014053919dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-oparu-5485-3dc.identifier.urn
GNDGraphentheoriedc.subject.gnd
GNDDominanzzahldc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
InstitutionInstitut für Optimierung und Operations Researchuulm.affiliationSpecific
Grantor of degreeFakultät für Mathematik und Wirtschaftswissenschaftenuulm.thesisGrantor
DCMI TypeTextuulm.typeDCMI
CategoryPublikationenuulm.category
Bibliographyuulmuulm.bibliographie


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