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dc.contributor.authorWarren, Samantha
dc.date.accessioned2018-03-27T22:29:00Z
dc.date.available2018-03-27T22:29:00Z
dc.date.issued2016-05
dc.identifier.urihttp://hdl.handle.net/11122/8223
dc.descriptionMaster's Project (M.S.) University of Alaska Fairbanks, 2016en_US
dc.description.abstractThe vertex arboricity of a graph is the minimum number of colors needed to color the vertices so that the subgraph induced by each color class is a forest. In other words, the vertex arboricity of a graph is the fewest number of colors required in order to color a graph such that every cycle has at least two colors. Although not standard, we will refer to vertex arboricity simply as arboricity. In this paper, we discuss properties of chromatic number and k-defective chromatic number and how those properties relate to the arboricity of trianglefree graphs. In particular, we find bounds on the minimum order of a graph having arboricity three. Equivalently, we consider the largest possible vertex arboricity of triangle-free graphs of fixed order.en_US
dc.language.isoen_USen_US
dc.subjectGraph coloringen_US
dc.subjectRandom graphsen_US
dc.subjectGraph theoryen_US
dc.titleVertex arboricity of triangle-free graphsen_US
dc.typeOtheren_US
dc.type.degreems
dc.identifier.departmentDepartment of Mathematics and Statistics
dc.contributor.chairGimbel, John
dc.contributor.committeeFaudree, Jill
dc.contributor.committeeAllman, Elizabeth
refterms.dateFOA2020-03-05T15:00:50Z


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