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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01jw827f42s
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dc.contributor.advisorLiu, Chun-Hung-
dc.contributor.advisorChudnovsky, Maria-
dc.contributor.authorShi, Jessica-
dc.date.accessioned2018-08-20T17:46:22Z-
dc.date.available2018-08-20T17:46:22Z-
dc.date.created2018-04-30-
dc.date.issued2018-08-20-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01jw827f42s-
dc.description.abstract3-coloring is a classically difficult problem, and as such, it is of interest to consider the computational complexity of 3-coloring restricted to certain classes of graphs. \(P_t\)-free graphs are of particular interest, and the problem of 3-coloring \(P_8\)-free graphs remains open. One way to prove that 3-coloring graph class \(\mathcal{G}\) is polynomial is by showing that for all \(G \in \mathcal{G}\), there exists a constant bounded dominating set in \(G\); that is to \(G\) contains a dominating set \(S\) such that \(|S| \leq K_\mathcal{G}\) for constant \(K_\mathcal{G}\). In this paper, we prove that there exist constant bounded dominating sets in subclasses of \(P_t\)-free graphs. Specifically, we prove that excepting certain reducible configurations which can be disregarded in the context of 3-coloring, there exist constant bounded dominating sets in \(\{P_6, \textrm{triangle}\}\)-free and \(\{P_7, \textrm{triangle}\}\)-free graphs. We also provide a semi-automatic proof for the latter case, due to the algorithmic nature of the proof.en_US
dc.format.mimetypeapplication/pdf-
dc.language.isoenen_US
dc.titleDominating sets in graphs with no long induced pathsen_US
dc.typePrinceton University Senior Theses-
pu.date.classyear2018en_US
pu.departmentMathematicsen_US
pu.pdf.coverpageSeniorThesisCoverPage-
pu.contributor.authorid961070654-
pu.certificateApplications of Computing Programen_US
Appears in Collections:Mathematics, 1934-2020

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